_TL_^J.  ^    „„„,.,.............    ,    .,    ,    -    -  •.  n_jyJjT_j    "    I-..-.  :P  .-.-_- 


REESE  LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


A    HANDBOOK 


ON 


REINFORCED 
CONCRETE 


FOR    ARCHITECTS 
ENGINEERS,    AND     CONTRACTORS 

BY 

F.   D.  WARREN 

MASSACHUSETTS  INSTITUTE  TECHNOLOGY,  1900 


NEW 

D.    VAN    NOSTRAND    COMPANY 
1906 


REESE 


l> 


COPYRIGHT,  1906,  BY 
D.   VAN   NOSTRAND  COMPANY 


Stanbope  press 

p.    H.GILSON     COMPANY 
BOSTON.      U.S.A. 


PREFACE. 


IN  preparing  this  volume,  I  have  endeavored  to 
produce  a  reference  handbook  that  would  be  par- 
ticularly adapted  to  the  wants  of  architects,  en- 
gineers, and  contractors.  Appreciating  the  value 
of  a  reference  book  to  a  designer  in  any  of  these 
branches,  and  especially  when  business  methods 
and  competition  demand  an  economy  of  time, 
such  a  choice  in  preference  to  a  text-book,  re- 
sulted. All  clue  care  has  been  exercised  to  avoid 
conflicts  with  data  compiled  in  the  many  valuable 
text-books  on  the  subject. 

It  was  purposed  to  produce  a  work  treating 
upon  a  general  form  of  design  rather  than  upon 
any  one  particular  or  patented  system,  but  to 
which  any  of  the  latter  may  be  applied.  The 
treatment  of  the  many  phases  entering  the  de- 
sign has  been  carried  out  along  well-known  for- 
mulae based  upon  the  theory  of  elasticity,  but 
modified  by  the  usual  assumptions,  such  as  the 
"conservation  of  planes"  and  "Hookes'  Law," 
and  not  upon  empirical  formula?  based  upon  ex- 
periments. Attention  should  be  called  to  the  fact 
that  before  applying  the  theory  of  elasticity  to 
any  particular  part  of  the  design,  a  sufficient 
number  of  tests  were  carried  out  along  this  basis 

5 

144173 


6  PREFACE. 

to  approve  it,  and  determine  the  coefficients  and 
constants. 

The  book  is  divided  into  four  parts:  Part  I 
gives  a  general  but  concise  resume  of  the  subject 
from  a  practical  standpoint,  bringing  out  some  of 
the  difficulties  met  with  in  practice,  and  suggest- 
ing remedies.  Under  Part  II  is  compiled  a  series 
of  tests  justifying  the  use  of  various  constants  and 
coefficients  in  preparing  the  tables  under  Part  III, 
as  well  as  bearing  out  the  theory  of  elasticity. 
Part  III  contains  a  series  of  tables  from  which  it 
is  hoped  the  designer  may  obtain  all  necessary 
information  to  meet  the  more  common  cases  in 
practice.  It  was  not  intended  to  cover  the  more 
intricate  designs,  as  this  is  a  feature  that  requires 
considerable  thought  and  time,  both  of  which  may 
be  profitably  applied.  Part  IV  treats  of  the  de- 
sign of  trussed  roofs  from  a  practical  standpoint. 

Finally,  if  this  volume  will*  tend  to  do  away 
with  the  use  of  some  of  the  "empirical  formulae" 
and  "rule  of  thumb'7  methods  of  designing  rein- 
forced concrete  structures,  and  tend  to  concen- 
trate all  toward  a  standard  and  universal  system, 
as  well  as  remove  some  of  the  prejudicial  influ- 
ences at  work  tending  to  demerit  its  worth  be- 
cause of  unfamiliarity  with  its  design,  it  will  have 
accomplished  its  purpose  in  the  mind  of  the 
writer. 


CONTENTS. 


PART  I. 

PAGES 

Tensile  Strength  of  Cement .  13 

Classification  of  Trap-rock  Sizes .  19 

Caring  for  Crushed  Stone  upon  the  Works 19 

Sand      22 

Proportion  of  Ingredients  for  the  Various  Mixes  ...  22 

Incorporation 26 

Protecting  Newly-laid  Work 32 

PART  II. 

Tensile  Strength  of  Concrete-Steel 37 

Test  of  Beam  No.  1 40 

Test  Beam  No.  2 43 

Cut  Showing  Failure  of  Beam  No.  1 45 

Cut  Showing  Failure  of  Beam  No.  2 45 

Remarks  Concerning  Tests  No.  1  and  No.  2 46 

Cut  Showing  Arrangement  of  Apparatus  for  Conduct- 
ing Tests  No.  1  and  No.  2 ,.-..     47 

Floor  Tests  Nos.  1-13 49-57 

Results  of  Floor  Tests  Nos.  1-13 58-59 

Remarks  Concerning  Floor  Tests 60 

Floor  Tests  Nos.  86  and  14 61-62 

Roof  Test  No.  22 63 

Remarks  upon  Plots  Showing  the  Relationship  between 

Expansion  and  Temperature 64 

Plot  Showing  Expansion  in  Fifty  Feet 65 

Plot  Showing  Expansion  hi  Thirty  Feet 67 

Conclusions 68 

Combined  Plot  Showing  Expansion  in  Ten  Feet  ...  69 

7 


8  CONTENTS. 

PART   III. 

PAGES 

Description  of  Table  I 75 

Tables  Giving  Safe   Bending  Moments  for  Different 

Sizes  of  Beams  or  Girders,  Called  Table  I 82-94 

Description  of  Tables  la  and  16 95-97 

Tables  Giving  Safe  Bending  Moments  for  Different 
Sizes    of    Continuous    Girders    (with    Two    Spans), 

Called  Table  la 98-105 

Key  to  Using  Tables  I,  la,  16,  and  II     .......        106 

Tables  Giving  Safe  Bending  Moments  for  Different 
Sizes  of  Continuous  Girders   (with  Three  or  More 

Spans),  Called  Table*  16 107-114 

Description  of  Table  II      • 115-116 

Tables    Giving    Safe    Loading    for    Different    Spans, 

Called  Table  II 117-128 

Description  of  Table  III 129-137 

Tables  Giving  Safe  Shearing  Forces  for  Different  Sizes 

of  Beams  or  Girders,  Called  Table  III 138-144 

Description  of  Table  IV 145-146 

Tables  Giving  Safe  Spans  for  Different  Sizes  of  Beams 
or  Girders,  Allowing  a  Safe  Deflection  of  3  ^Q  of  Span, 

Called  Table  IV 147-149 

Description  of  Table  V 150 

Table   Giving   Safe   Bending   Moments   for   Different 

Thicknesses  of  Floors,  Called  Table  V 152 

Description  of  Table  Va 153 

Table    Giving    Amount    of    Steel    to    Resist    Various 

Temperature  Changes  in  Floors,  Called  Table  Va     .        154 

Description  of  Table  VI 155 

Table  Giving  Safe  Loadings  and  Spans  for  Different 

Thicknesses  of  Floors,  Called  Table  VI 157-165 

Description  of  Table  VII 166 

Tables  Giving  Safe  Loads  for  Different  Sizes  of  Col- 
umns, Called  Table  VII 167-169 

Description  of  Table  VIII 170 


CONTENTS.  y 

PAGES 

Comparative    Costs,  —  Beams    for    Equal    Strength, 

CaUed  Table  VIII      172-173 

Description  of  Table  IX 174 

Comparative    Costs,  —  Floors    for    Equal    Strength, 

Called  Table  IX 175 

Description  of  Table  X 176 

Comparative    Costs,  —  Floors    for    Equal    Deflection, 

Called  Table  X 173 

Description  of  Table  XI 177 

Comparative   Costs,  —  Columns  for   Equal   Strength, 

Called  Table  XI 178-1  S3 

Cost  of  Reinforced  Concrete  Columns,  Octagonal  Sec- 
tion, for  Different  Sizes 184-186 

Amounts  of  Cement,  Sand,  and  Stone  Required  for 
Concrete  Mixtures  of  Various  Proportions,   Called 

Table  XII 187-188 

Description  of  Table  XIII ......       189 

Relative  Strength  of  Different  Proportions  of  Mixture, 

Called  Table  XIII 190 

PART  IV. 

Trussed  Roofs 193-200 

Reinforced  Concrete  Roofs 201-202 

Description  of  Table  XIV "...    .    .    .       202 

Roof  Designs,  Called  Table  XIV      .    .    203-205 

Description  of  Table  XlVa 205 

Costs  of  Roofs,  Called  Table  XlVa 206 

Description  of  Table  XV 206 

Table  XV.  —  Truss  Designs 208-213 

Description  of  Table  XVa 214 

Weights  of  Trusses.  —  Table  XVa  .  -r-r~-.    ....    215-216 

Description  of  Plots .    .        217 

Plots  of  Costs.—  Table  XV      218-222 

Description  of  Table  XVI 223 

Table  XVI.  —  Truss  Designs 224-230 

Description  of  Table  XVIa 231 


10  CONTENTS. 

PAGES 

Weights  of  Trusses.  —  Table  XVIa 232 

Plots  of  Costs.  —  Table  XVI 233-237 

Description  of  Table  XVII 238 

Table  XVII.  —  Truss  Designs 239-242 

Plot  of  Costs.  —  Table  XVII .       243 

Description  of  Table  XVIIa 244 

Weights  of  Trusses.  —  Table  XVITa 244 

Description  of  Table  XVII6 245 

Table  XVII6.  —  Truss  Designs 246-248 

Plots  of  Costs.  —  Table  XVII .       249 

Weights  of  Trusses.  —  Table  XVII^ 250 

Description  of  Table  XVIIc      251 

Table  XVIIc.  —  Truss  Designs 251-253 

Description  of  Table  XV lid 254 

Table  XVIId.  —  Truss  Designs 254-256 

General  Description  of  Trusses  of  Types  Treated  under 

Tables  XVII-XVIId 257 

Description  of  Table  XVIII 258 

Plot  to  Determine  Factor  K  in  Formula     ....'..       261 

Table  XVIII.  —  Truss  Designs 262-266 

Plot  of  Costs.  —  Table  XVIII 267 

Plots  Showing  Comparative  Costs  of  Different  Kinds 

of  Trusses 268-269 

Weights  of  Trusses.  —  Table  XVIIIa 270-271 


PAET   I. 
TENSILE  STRENGTH  OF  CEMENT. 


11 


HANDBOOK   ON 

REINFORCED    CONCRETE. 


THE  tensile  strength  of  a  cement  enters  into  the 
design  of  a  reinforced  concrete  structure  only 
indirectly.  However  indirectly  as  it  may  be,  it  is 
of  the  utmost  importance,  since  the  possibility  of 
realizing  a  satisfactory  design  depends  entirely 
upon  the  obtaining  of  a  satisfactory  value  for  the 
same.  The  prime  object  of  knowing  the  tensile 
strength  of  a  given  cement  which  is  being  used  on 
works  of  magnitude,  is  to  safeguard  the  owners 
that  they  are  receiving  from  the  makers  the  qual- 
ity of  cement  specified  by  the  architects.  Thus  it 
may  "be  seen  thatrthe  time  when  this  factor  enters 
the  problem  is  not  during  the  design,  but  during 
the  erection  of  the  plant. 

SPECIFICATIONS.  —  For  instance,  a  cement  is 
sometimes  specified  to  be  calcined  from  given  pro- 
portions of  given  constituents,  which  are  known 
to  render  a  first-class  cement  of  a  high  tensile 
strength.  This  measure,  although  used  for  cau- 
tion, seems  too  exacting  upon  the  cement  makers, 
as  doubtless  there  are  secrets  in  the  manufacture 
of  the  cement,  known  only  to  the  makers,  which 
are  of  great  value  to  it,  and  which  would  be  en- 
tirely upset  by  such  stringent  requirements.  It 

13 


14        HANDBOOK   ON   REINFORCED    CONCRETE. 

should  rather  be  specified,  and  more  properly,  that 
the  cement  delivered  on  the  works  must  stand  a 
certain  tensile  strength  per  square  inch  when 
made  into  the  standard  briquette  of  neat  cement, 
and  allowed  to  set  in  air  for  a  given  time  before 
testing,  or  shall  stand  another  stated  stress  per 
square  inch  when  made  as  before,  but  allowed  to 
take  its  initial  set  in  air,  and  then  immersed,  and 
allowed  to  remain  a  stated  time  in  water  of  a 
given  temperature  before  testing.  Sometimes  one 
or  the  other  of  these  figures  of  tensile  strength 
per  square  inch  is  given,  and  the  second  given  as 
a  ratio  in  terms  of  the  first  that  must  not  vary 
over  a  certain  amount.  In  either  case,  the 
briquette  should  take  its  initial  set  without  a 
perceptible  rise  in  temperature. 

Again,  it  may  be  specified  that  the  cement  in 
question  shall  be  thoroughly  burned  during  cal- 
cination. To  satisfy  ourselves  in  this  respect,  we 
have  but  to  carefully  watch  the  above-mentioned 
briquettes  or  other  samples  while  setting.  Should 
these  show  a  rise  in  temperature  while  setting, 
we  are  at  once  convinced  that  the  cement  was  not 
properly  burned.  Yet,  if  this  fact  be  lost  sight  of 
at  this  time,  the  results  from  the  tensile  strength 
will  show  that  something  is  wrong,  and  if  this 
something  reduces  the  test  below  the  fixed  speci- 
fied amount,  we  are  justified  in  condemning  the 
lot,  provided  sufficient  tests  to  give  an  average  of 
the  lot  show  the  deficiency,  without  troubling 
ourselves  as  to  the  exact  cause. 


TENSILE  STRENGTH   OF   CEMENT.  15 

Thirdly,  it  may  be  specified  that  the  cement  be 
ground  to  a  certain  degree  of  fineness  by  requiring 
a  certain  part,  or  all,  to  pass  a  sieve  of  specified 
number,  and  all,  or  but  a  small  per  cent,  to  be 
retained  on  a  second  sieve  of  smaller  mesh.  If 
the  cement  be  improperly  or  rather  too  coarsely 
ground,  there  will  be  grains  in  more  or  less  num- 
bers of  too  large  proportions  to  bond  with  the 
finer  and  more  uniform  mass,  and  the  only  mis- 
sion these  can  have  is  to  act  as  so  much  sand, 
and  necessarily  lower  the  tensile  strength.  So, 
again  we  resort,  or  should  resort,  to  the  results  of 
the  tensile  tests.  But  this  fault  may  also  be  de- 
tected by  weighing,  for  it  is  generally  known  that, 
bulk  for  bulk,  a  coarser  ground  grade  will' weigh 
in  excess  over  a  finer  ground  grade.  It  is  not 
practical  to  be  too  severe  with  this  measure,  for 
there  is  danger,  if  the  brand  be  too  finely  ground, 
and  especially  if  the  sand  used  be  fairly  coarse, 
that  the  particles  of  cement  will  be  too  small  to 
fill  the  voids  in  the  sand,  unless  we  make  our- 
selves doubly  sure,  and  use  a  larger  ratio  of  cement 
to  overcome  the  danger,  which,  to  say  the  least,  is 
a  remedy  too  extravagant  for  the  most  scrupulous. 

Fourthly,  caused  by  the  improper  mixing  of 
materials,  or  by  insufficient  burning  during  calci- 
nation, a  pat  of  neat  cement  when  worked  up  in 
the  hand,  and  placed  upon  a  piece  of  glass  under 
water,  will  creep  and  draw  up  along  its  outside 
perimeter  where  it  meets  the  glass.  Also,  pri- 
marily due  to  the  same  cause,  a  pat  of  neat  cement 


16   HANDBOOK  ON  REINFORCED  CONCRETE. 

made  as  before,  and  placed  under  water,  will  blow, 
liberating  bubbles  of  air  and  indicating  chemical 
action  taking  place.  Both  these  influences  tend 
to  lower  the  tensile  strength. 

Attention  has  already  been  called,  first  to  the 
mixture  of  constituents  composing  the  cement; 
second,  to  the  proper  burning  of  these  constitu- 
ents; and  thirdly,  to  the  degree  of  grinding  after 
the  calcining  process.  These  I  consider  the  three 
important  steps  in  the  making  of  cement,  and  a 
slip  in  any  of  these  during  manufacture  renders 
a  product  totally  unfit  for  use.  To  guard  against 
the  use  of  .any  lot,  deficient  in  this  manner,  and 
especially  in  reinforced  concrete  construction,  is 
the  prime  object  of  what  has  been  written;  and 
finally,  as  a  safeguard,  I  make  an  urgent  appeal 
for  the  more  general  adoption  of  making  tensile 
tests,  and  to  an  extent  to  give  a  fair  average  of 
the  lot  in  order  to  show  up  the  quality  of  the 
cement  which  is  being  used  at  any  time  upon  the 
works. 

Now,  the  brand  of  cement  which  has  been 
specified,  and  which  is  supposed  to  meet  all  the 
requirements,  has  arrived  on  the  works.  To  be 
sure,  one  has  his  faculties  of  sight  and  feeling, 
which  can  be  used  to  good  advantage  in  passing 
superficial  judgment  upon  the  lot,  provided  his 
judgment  has  had  the  necessary  training  through 
experience.  For  instance,  the  color  of  the  lot  will 
tell  the  more  experienced  in  a  general  way  the 
composition  of  the  mixture,  when  the  locality  from 


TENSILE    STRENGTH    OF    CEMENT.  17 

which  the  constituents  were  taken  is  known,  since 
the  ingredients  vary  greatly  in  texture  in  different 
localities.  This,  at  the  best,  can  be  of  only  pass- 
ing importance,  as  the  exact  proportions  of  the 
constituents,  which  so  largely  affect  the  chemical 
reaction  to  make  the  proper  compound,  will  not 
always  appeal  to  the  eye  in  the  same  way  when 
so  many  things  enter  into  the  process  which  may 
upset  any  fast  rules.  But  very  fortunately  there 
is  the  privilege  of  applying  the  tensile  tests  to 
satisfy  oneself  that  the  combination  of  ingredients 
is  such  as  not  to  impair  the  strength. 

Again,  the  sense  of  feeling  may  be  used.  The 
expert  can,  by  running  his  hand  through  the  lot 
and  by  rubbing  together  the  particles,  in  a  meas- 
ure tell  whether  there  are  too  many  unground  or 
too  coarsely  ground  particles  to  affect  the  results 
so  as  not  to  meet  the  requirements.  Once  more, 
if  one  is  not  thus  skilled,  and  in  all  cases  as  a 
precautionary  measure,  the  tensile  strength  should 
be  relied  upon  to  determine  whether  the  lot  is  not 
too  diluted  by  coarse  particles,  before  accepting 
the  lot.  Thus,  one  has  his  faculties  to  guard  him 
against  two  of  the  many  faults;  and  how  often 
does  not  this  suffice  to  accept  a  lot,  which,  had 
tests  been  taken,  would  never  have  been  unloaded 
from  the  car. 

In  summing  up,  it  may  be  expected  that  two 
lots  of  cement,  made  .from  the  same  ingredients, 
taken  from  the  same  locality,  and  mixed  in  the 
same  proportions,  will,  if  made  into  neat  cement 


18        HANDBOOK   ON   REINFORCED    CONCRETE. 

briquettes,  using  the  same  care  as  regards  mixing, 
proportion  and  temperature  of  water  used,  and 
the  place  and  conditions  of  setting,  give  fairly 
uniform  results  by  tensile  tests.  Hence,  it  re- 
mains for  the  architect  merely  to  fix  upon  the 
tensile  strength  of  a  cement  known  to  be  good 
when  allowed  to  set  for  a  given  time  under  given 
conditions,  and  to  see  to  it  that  every  shipment, 
when  a  sufficient  number  of  samples  have  been 
taken  to  warrant  the  average  lot,  shall  meet  the 
requirements,  when  the  briquettes  have  been  made, 
set,  and  tested  under  similar  conditions  which 
governed  the  standard.  No  little  stress  should  be 
laid  upon  this  matter,  for  it  seems  to  the  writer, 
that  in  works  of  magnitude,  where  every  other 
precaution  is  taken  to  insure  the  obtaining  of 
proper  materials,  and  where  a  large  amount  of 
money  is  at  stake,  this  primary  function  of  qual- 
ity and  endurance  to  the  structure,  second  not 
even  to  workmanship  of  mixing  and  deposit- 
ing the  concrete,  should  not  be  overlooked  nor 
deemed  too  expensive  to  maintain  throughout  the 
time  during  which  the  concrete  is  being  placed. 
By  what  has  just  been  said,  do  not  imagine  that 
the  workmanship  is  a  matter  of  inconsiderable 
importance.  On  the  contrary,  it  is  second  in  im- 
portance only  to  the  grade  of  cement.  It  should 
be  remembered  that  the  life  and  endurance  of  the 
structure  are  dependent  upon  both  conditions,  and 
anything  lacking  in  one  cannot  be  compensated  for 
in  the  other,  and  the  whole  suffers  in  accordance. 


TENSILE  STRENGTH  OF  CEMENT.  19 

CLASSIFICATION  OF  TRAP  ROCK  SIZES. 

It  seems  to  the  writer  that  one  of  the  necessary 
steps  in  the  specifications  of  the  architect  is  to 
classify  the  sizes  of  trap  rock  that  may  properly 
be  used  in  the  different  parts  of  the  building. 
Thus,  it  may  be  arbitrarily  fixed  that  the  sizes  of 
rock  to  be  used  in  the  foundation  must  all  pass  a 
2J-inch  ring,  and  all  be  retained  on  a  1-inch 
screen.  For  exterior  walls  and  piers,  where  the 
sizes  of  the  same  will  permit  proper  rodding,  it 
may  be  specified  that  all  rock  shall  pass  a  1-inch 
and  all  be  retained  on  a  J-inch  screen.  For  gird- 
ers, beams,  and  floors  above  the  steel  members, 
also  for  columns,  all  rock  should  pass  a  screen  of 
J-inch  mesh,  and  all  be  retained  on  a  J-inch  mesh. 
Below  and  around  the  steel  members  in  girders, 
beams,  and  floors,  in  order  to  obtain  proper  rod- 
ding  and  perfect  work,  no  stone  should  be  used 
that  will  not  pass  a  screen  of  J-inch  mesh,  and 
should  include  everything  under  except  the  dust. 
This  is  ordinarily  known  as  pea  size. 

CARING  FOR  CRUSHED  STONE  UPON  THE  WORKS. 

Under  the  heading  of  Classification  it  may  be 
perceived  that  in  cases  where  a  crusher  is  used  on 
the  works,  all  grades  of  the  trap  rock  may  be 
used  from  2J  inch  down,  excluding  the  dust.  As 
screened,  the  different  grades  should  be  deposited 
in  bins  or  piles  properly  labeled,  so  there  can  be 


20   HANDBOOK  ON  REINFORCED  CONCRETE. 

no  mistake  made  by  the  man  in  charge  of  the 
mixer  or  the  different  gangs  of  men  when  there 
comes  a  call  for  a  change  in  mixture. 

If,  on  the  other  hand,  the  trap  rock  is  received 
on  the  works  by  the  carload,  it  should  be  seen  to 
that  each  carload  is  labeled  as  to  its  grade,  and 
that  it  is  unloaded  into  its  proper  bin  or  pile. 
As  a  safeguard  where  the  rock  is  received  by  the 
carload,  and  not  inspected  as  to  its  grade,  and 
especially  when  coming  from  an  unreliable  yard, 
it  is  well  to  run  the  rock  through  screens  so  ar- 
ranged and  spouted  beneath  that  the  different 
grades  reach  their  proper  piles. 

Accordingly,  four  bins  or  piles  will  be  required; 
and  if  circumstances  will  allow,  and  machine 
mixing  be  adopted,  the  hopper  feeding  the  mixer 
should  have  four  compartments.  Yet  this  is  not 
absolutely  necessary,  for  it  is  not  probable  that 
there  would  be  calls  at  any  one  time  for  the  four 
grades  from  any  one  mixer.  Before  charging  the 
hopper,  or  its  different  compartments,  it  is  abso- 
lutely necessary  that  the  rock  be  thoroughly 
washed  free  from  dirt  and  dust  in  order  that 
every  opportunity  may  be  given  to  the  cement  to 
completely  coat  the  exterior  surface. 

No  little  stress  should  be  laid  upon  this  matter 
of  classifying  the  different  grades  of  rock,  and 
keeping  each  within  its  sphere  for  its  proper  in- 
stallation in  the  building.  For  each  grade  of 
stone  there  is  a  definite  amount  of  sand  and  a 
fixed  proportion  of  cement  within  limits  required 


TENSILE    STRENGTH    OF    CEMENT.  21 

to  make  a  homogeneous  concrete;  and  without 
this  homogeneity  of  mass,  we  are  putting  weak 
links  in  the  chain,  just  as  would  be  done  provided 
we  allowed  poor  cement  to  enter.  As  there  is  a 
safeguard  against  this  latter,  so  there  is  against 
allowing  the  different  grades  to  be  interchanged, 
and  this  is  care.  To  be  more  explicit  in  regard  to 
the  consequences  which  are  bound  to  exist  with- 
out this  due  amount  of  care,  let  me  add:  Sup- 
posing the  mixture  which  is  being  run  through  the 
mixer  is  for  beams  or  floors,  and  the  measuring 
devices  are  set  for  the  proper  amount  of  sand  and 
cement  for  a  j— J  gauge  stone.  Through  careless- 
ness, let  us  suppose  that  the  mixer  hopper  has 
been  charged  with  a  few  buckets  of  the  2J-1 
gauge  stone  along  with  the  J— J  gauge..  When  this 
enters  the  measuring  hopper,  there  is  neither  time 
nor  ready  means  of  changing  the  sand  and  cement 
to  agree,  provided  the  tender  knew  enough.  Con- 
sequently, the  larger  stone  goes  through  with  the 
proportions  of  sand  and  cement  for  the  smaller 
stone,  —  in  other  words,  with  voids  unfilled,  and 
the  concrete  far  from  being  homogeneous.  But  the 
trouble  does  not  end  here.  The  mass,  already 
diluted,  is  deposited  upon  the  floor,  and  shoveled 
into  the  beams,  and  other  men  follow  along  with 
tamps  to  rod  the  same  into  place.  Although  going 
through  their  usual  mechanical  motions,  what  is 
the  result?  With  the  large  size  of  stone  it  is 
impossible  to  work  them  into  a  small  beam,  or 
around  steel  members  without  allowing  voids  to 


22        HANDBOOK    ON    REINFORCED    CONCRETE. 

form,  and  again  we  are  sacrificing  homogeneity. 
Thus  a  slip  in  one  respect  has  weakened  the  chain 
twofold. 

SAND. 

Where  practicable,  two  grades  of  sand  should 
be  specified,  —  one  to  be  a  very  coarse  and  angu- 
lar crushed  quartz;  the  other  to  be  a  finer  river  or 
bank  sand,  also  angular.  The  proportions  of  the 
two  may  be  determined  thus :  Take  a  given  bulk  of 
the  coarse  sand,  and  determine  the  voids  after  the 
manner  described  later  on.  The  ratio  of  the  voids 
to  the  original  volume  of  coarse  sand  will  be  the 
ratio  of  fine  sand  to  coarse  to  be  used.  The  two 
grades  of  sand  should  be  measured  out,  thor- 
oughly, mixed  in  the  above  proportions,  washed 
free  from  dirt,  and  deposited  in  a  pile  or  bin  ready 
for  the  sand  compartment  of  the  mixer. 

If  but  one  grade  of  sand  can  be  conveniently 
obtained,  it  should  be  of  medium  grade,  very 
irregular  as  to  size  of  granules,  and,  of  course, 
sharp  and  angular.  Besides,  it  should  be  tested 
at  frequent  intervals  for  voids  to  insure  the  proper 
amount  of  cement  at  all  times  to  obtain  a  homo- 
geneous mass. 

PROPORTIONS  OF  INGREDIENTS  FOR  THE  VARIOUS 
MIXES. 

Now  that  we  have  the  ingredients  for  making 
the  concrete,  —  namely,  the  cement,  which  has 


TENSILE    STRENGTH    OF   CEMENT.  23 

passed  the  tensile  requirements,  the  cleaned  sand 
in  its  compartment,  and  the  rock  in  its  various 
compartments  fixed  by  the  arbitrary  grades  es- 
tablished, —  next  comes  the  fixing  of  the  ratio  of 
these  ingredients,  determined  by  the  grade  of  rock 
and  the  grade  of  sand,  to  make  a  proper  concrete 
as  regards  homogeneity. 

To  do  this,  take  a  form  impervious  to  water, 
that  will  hold  just  one  cubic  yard  by  its  actual 
inside  dimensions.  Fill  this  shovel  by  shovel  with 
the  grade  of  stone  from  which  is  required  the 
proper  mix,  compacting  the  same  as  much  as  pos- 
sible. Then  obtain,  by  measuring  the  volume  of 
water  required  to  fill  the  voids  between  the  stones, 
the  amount  and  ratio  of  the  voids  to  the  whole. 
Then  remove  the  stone  and  water,  and  with  the 
volume  of  sand  as  just  determined  by  the  volume 
of  water  thoroughly  mixed  with  the  measured 
cubic  yard  of  stone,  replace  the  mixture  into  a 
water-tight  form  of  the  same  width  and  length, 
but  of  somewhat  greater  depth  than  before,  tamp- 
ing the  same  well  as  it  is  placed  shovel  by  shovel 
into  the  form.  Then  the  increase  in  depth  will 
give  the  relative  increase  in  proportions  by  add- 
ing the  sand.  After  leveling  and  tamping  the 
contents  into  the  form,  measure  again  the  amount 
of  water  required  to  fill  the  remaining  voids  just 
to  the  level  of  the  top  of  the  sand  and  stone. 
Remove,  and  with  other  stone  of  the  same  grade, 
and  other  sand  of  like  grade,  and  both  of  the 
same  volumes  already  determined,  and  with  the 


24        HANDBOOK    ON    REINFORCED    CONCRETE. 

volume  of  cement  determined  by  the  last  measure- 
ment of  water  added,  all  thoroughly  mixed,  re- 
place the  same  into  the  measuring  form  shovel  by 
shovel,  tamping  and  leveling  as  before.  Again 
note  the.  increase  of  height  and  hence  the  increase 
of  volume  by  adding  the  cement.  Undoubtedly 
we  could  add  a  considerable  volume  of  water  to 
the  mass  before  same  stood  at  the  level  of  the 
mixture  in  the  form,  showing  voids  remaining  un- 
filled. These,  however,  are  due  to  improper  mix- 
ing of  the  materials,  and  insufficient  ramming  into 
place,  and  should  be  compensated  for  as  stated 
farther  on.  Now  we  have  determined  not  only 
the  proper  ratio  of  ingredients  for  the  grade  of 
stone  and  sand  in  question  to  make  a  homo- 
geneous mix,  but  also  the  ratio  of  the  final  to  the 
initial  volume,  which  will  be  from  1.1  to  1.3, 
depending  upon  the  grade  of  stone.  So  we  may 
expect  that  every  cubic  yard  of  crushed  stone  will 
fill  a  space  in  the  structure  of  1.1  to  1.3  cubic 
yards  after  the  same  has  been  made  into  its  proper 
mix  of  concrete. 

After  water  has  been  added,  which  should  be 
enough  to  make  a  plastic  mass  in  order  to  insure 
the  filling  of  the  mold  properly,  and  especially 
plastic  where  it  is  difficult  to  incorporate  the  mass 
thoroughly  by  rodding,  tamping,  and  rolling,  the 
mass  will  have  gained  in  bulk  nearly  in  proportion 
to  the  water  added,  provided  that  the  voids  have 
been  properly  filled  when  mixed  dry,  that  the 
cement  is  in  proper  condition  as  already  deter- 


TENSILE    STRENGTH    OF    CEMENT.  25 

mined  by  the  tensile  tests,  and  that  the  rock  and 
sand  have  been  thoroughly  wetted  beforehand,  as 
both  have  a  certain  avidity  for  water  depending 
upon  climatic  conditions.  This  gain  in  mass  will 
probably  amount  to  2  to  5  per  cent  over  its  volume 
when  dry,  depending  upon  the  amount  of  water 
added.  While  setting,  this  water  is  gradually  ab- 
sorbed by  chemical  action  and  outside  influences, 
and  the  mass  gradually  diminished,  tending  to 
assume  its  normal  state  when  dry.  Thus,  what  is 
generally  known  as  the  shrinkage  of  concrete  dur- 
ing set  is  merely  the  tendency  of  the  mass  to 
attain  its  original  bulk  when  dry. 

As  previously  mentioned,  voids  remain  in  the 
mass  after  seemingly  the  proper  proportions  of 
ingredients  have  been  fixed.  These  are  bound  to 
occur,  for  in  practice,  because  of  so  many  variables 
entering  to  upset  the  best  of  calculations,  it  is 
impossible  to  obtain  nearly  the  results  which  are 
obtained  when  determining  the  proportions.  Then 
again,  when  the  plastic  mass  is  deposited  into  the 
molds,  it  is  impossible  to  prevent  a  leakage  of 
water,  and  this  leakage  will  carry  away  with  itself 
some  of  the  cement.  To  overcome  such  difficul- 
ties, which  must  necessarily  happen,  we  have  to 
resort  to  a  factor  of  safety,  as  we  might  term  it, 
by  adding  to  the  proportions  already  determined 
an  excess  of  cement  varying  from  5  to  10  per  cent 
as  best  seems  required  to  meet  each  particular 
case. 

In  what  has  been  said,   it  may  appear  how 


26         HANDBOOK    ON    REINFORCED    CONCRETE. 

difficult  it  is  to  obtain  the  proper  proportions  of 
ingredients,  even  when  the  utmost  care  is  taken. 
Hence,  all  the  more  reason  for  being  careful. 

In  summing  up  the  matter  of  proportions  of 
ingredients,  we  may  derive  some  general  figures, 
which  we  will  term  mixes,  all  of  which  can  be  only 
approximate,  and  all  subject  to  the  variables 
already  mentioned  tending  to  change  them  more 
or  less.  For  instance,  for  the  2  J-inch- 1-inch 
grade  of  rock,  the  proportions  of  cement  to  sand 
and  to  stone  should  be  about  1-2J-5.  This  we 
will  term  a  1-2J-5  mix.  For  the  1-inch-J-inch 
grade  of  work,  a  1-2-4  mix  seems  to  be  about  the 
proper  thing  in  round  numbers.  Likewise  from 
the  f-inch-J-inch  grade,  a  1-1 J-3  mix  results,  and 
from  the  pea-size  grade,  a  1-1-2  mix  results. 

By  comparing  these  mixes  with  what  has  been 
said  concerning  the  proper  sizes  of  rock  for  indi- 
vidual locations  in  the  structure,  it  can  be  readily 
seen  that 

Foundations  require  the 1-2^-5  mix 

Outside  walls,  piers,  etc.,  require  the 1-2  -4  mix 

Girders,  beams,  floors,  and  roofs  above  the  steel 

members,  also  inside  columns,  require  the  .  1-1  $-3  mix 
Girders,  beams,  floors,  and  roofs  below  the  steel 

require  the 1-1  -2  mix 

Wearing  surface  for  floors  requires  ....  1  cement-2  sand 

INCORPORATION. 

After  the  different  mixes  have  been  settled 
upon,  and  we  are  sure  these  are  coming  from  the 
mixer  in  due  form,  the  next  important  step  seems 


TENSILE   STRENGTH    OF    CEMENT.  27 

to  be  the  distribution  of  these  mixes  into  their 
proper  places.  Whatever  else  goes  wrong,  it  is 
necessary  to  have  the  1-1-2  mix  to  work  around 
the  steel  in  the  beams  and  girders  and  for  the  first 
spreading  upon  the  floor  to  receive  the  steel.  If 
not,  the  penalty  is  paid  later  on,  when  the  false 
work  is  stripped,  and  a  honeycombed  surface 
presents  itself.  There  is  no  excuse  for  the  1-2J-5 
mix  ever  reaching  the  superstructure,  so  we  may 
eliminate  this  from  our  cares.  It  should  be  care- 
fully watched  that  the  1-1^-3  and  the  1-2-4  mixes 
reach  their  destination,  but  the  danger  resulting 
from  the  interchanging  of  these  two  mixes  is  the 
least  of  any  of  the  combinations. 

That  proper  incorporation  should  result  by  care- 
ful and  scientific  rodding,  cutting,  tamping,  and 
rolling,  the  plastic  mass  must  be  a  realized  fact, 
and  this  can  be  so  only  by  using  all  care  and  by 
putting  the  proper  man  in  the  proper  place.  But 
first  of  all,  before  we  can  rod,  tamp,  or  roll  the 
mass  successfully,  we  must  have  a  mass  that  is 
in  such  a  physical  state  as  can  be  so  rodded, 
tamped,  or  rolled.  By  this  is  meant  a  concrete 
made  from  a  moderately  slow-setting  cement,  one 
containing  the  proper  mix,  and  one  sufficiently 
plastic.  A  cement  that  will  begin  to  take  on  its 
initial  set  to  any  extent  within  half  an  hour  after 
mixing  has  no  place  in  the  superstructure  of  a 
building,  and  yet  how  often  do  we  see  such  a 
cement  in  use  that  will  set  up  so  hard  as  to 
require  hoeing  or  picking  out  of  the  bucket. 


28        HANDBOOK   ON    REINFORCED   CONCRETE. 

How  can  this  be  properly  rodded,  tamped,  or 
rolled?  The  time  of  thirty  minutes'  grace,  as  we 
may  term  it,  is  arbitrarily  fixed  upon  as  under 
ordinary  conditions ;  the  rodding,  tamping,  rolling, 
leveling,  and  walking  over  a  section  require  that 
amount  of  time  at  least,  before  it  can  be  left  for 
nature  to  take  her  course. 

In  many  cases  it  is  required  that  the  top  finish 
shall  be  floated  on  immediately  after  the  base  is 
laid.  This  seems  to  the  writer  quite  unscientific 
and  very  impracticable.  It  is  held  by  the  sup- 
porters of  this  method  that  the  strength  of  the 
floor  is  increased,  and  that  perfect  bond  between 
the  base  and  the  finish  is  realized.  That  this 
latter  is  accomplished,  no  one  can  dispute.  In 
regard  to  the  former  supposition,  there  seems  to 
be  just  grounds  to  take  exceptions.  If  any 
strength  is  gained  thereby,  it  is  by  adding  more 
area  to  the  concrete  to  resist  compression.  Al- 
ready, before  the  addition  of  the  1-inch  finish,  the 
floor  is  as  able  to  resist  compression  as  it  is  tension. 
Any  addition  of  strength  to  one  link  of  a  chain 
does  not  increase  the  durability  of  the  whole 
chain.  It  may  be  argued  that  this  will  increase 
the  moment  of  resistance  of  the  steel,  which  un- 
doubtedly would  be  true  if  it  could  be  practically 
realized,  but  this  is  not  the  weak  point  of  the  floor 
if  properly  designed.  The  weak  point  is  the  ad- 
hesion of  the  concrete  surrounding  the  steel  mem- 
bers. By  adding  the  finish  at  this  crucial  time, 
it  would  be  necessary  to  keep  walking  over  the 


TENSILE    STRENGTH    OF    CEMENT.  29 

soft  base,  which  has  already  begun  to  set;  and  in 
so  doing,  you  are  all  the  while  destroying  the 
bond  between  the  setting  concrete  and  the  steel, 
thus  impairing  the  adhesion  between  the  two, 
without  which,  the  steel  is  more  or  less  unsup- 
ported, and,  when  undergoing  tension  by  bending, 
may  be  so  separated  from  the  concrete  that  the 
latter  is  unable  to  take  the  stress,  caused  by  the 
elongation  of  the  steel  fibers  while  bending,  from 
the  steel.  In  other  words,  instead  of  having  a 
compact  mass  so  constrained,  one  member  by 
another,  that  any  stress  in  one  may  be  trans- 
mitted to  another,  and  the  entire  stress  distributed 
throughout  the  number  of  members,  we  have  a 
more  or  less  mutilated  and  disconnected  whole. 
All  our  former  carefulness  to  obtain  a  homogene- 
ous compact  mass  has  been  set  at  naught,  and  we 
are  only  undoing  what  we  have  already  tried  so 
hard  to  do.  Then  there  is  another  consideration. 
The  top  finish  should  be  considered  as  the  top 
floor  of  a  house  or  mill,  a  part  which  takes  the 
wear.  What  strength  it  imparts  to  the  lower 
floor,  we  do  not  stop  to  figure  or  think  of.  It  is 
put  there  for  one  sole  purpose,  to  take  wear,  no 
more  nor  less.  To  take  wear,  the  cement  finish 
should  be  uniform  throughout,  both  as  regards 
breadth  and  depth,  and  to  attain  this,  the  top 
surface  must  be  screeded  off  perfectly  level.  To 
do  this,  the  screeds  cannot  be  set  on  a  soft  surface 
and  the  same  leveled  both  ways  over  any  con- 
siderable amount  of  area  with  the  ordinary  level 


30        HANDBOOK    ON   REINFORCED    CONCRETE. 

and  straight  edge.  It  requires  the  accurate  work 
of  an  engineer  with  an  instrument  to  establish  a 
level  grade  by  setting  nails  in  the  base  floor  after 
the  latter  has  set  for  twelve  to  twenty-four  hours, 
and  for  careful  workmen  to  bring  the  screeds  to 
the  nails,  to  attain  anything  like  proper  results. 
Provided  the  mason  could  level  the  screeds  prop- 
erly, how  long  would  they  remain  so,  resting  as 
they  would  on  a  soft  base,  which  is  all  the  while 
being  disturbed  by  walking  over  it?  The  effect 
of  screeding  off  a  floor,  out  of  level,  is  for  the 
water  to  flow  by  gravity  to  the  low  places,  carry- 
ing with  it  cement  from  the  high  places.  The 
cement  which  has  collected  in  the  hollows,  after 
the  surface  has  been  floated  and  finished,  forms 
into  a  thin  skin  with  no  body,  and  instead  of 
bonding  with  the  particles  below,  seems  to  keep 
apart  from  them,  sets  slower,  and  later  on  when 
the  floor  is  put  in  use,  scales  off  by  wear.  The 
high  places  have  lost  a  considerable  amount  of 
the  cement  which  should  be  there  in  order  to 
float  and  trowel  the  same  to  a  smooth,  hard  sur- 
face, but  instead,  the  surface  is  rough  and  sandy, 
in  such  condition  that  trucking  and  wear  keep 
removing  the  rough  particles;  hence  the  spot  or 
spots  grow  more  and  more  uneven,  and  more 
extensive. 

Again,  the  water  insuring  a  proper  set,  has  run 
from  the  high  places  to  the  low  places,  allowing 
the  latter  to  become  oversupplied.  Consequently, 
the  surface  is  not  uniform,  and  when  one  part  is 


TENSILE    STRENGTH    OF   CEMENT.  31 

ready  for  floating  or  smoothing,  another  part  is 
not  ready,  thereby  increasing  the  chances  of  allow- 
ing one  part  to  go  too  long  to  be  properly  worked. 
Ultimately,  the  high  places  set  faster  than  they 
should,  because  of  insufficient  water,  while  for  the 
opposite  reason,  the  low  places  do  not  set  so 
quickly.  The  only  thing  that  can  be  expected, 
under  such  conditions,  is  a  network  of  cracks 
between  the  two  surfaces,  and  these  expectations 
are  usually  realized.  Now  what  has  been  gained? 
Strength  may  have  been  added  to  the  floor  by 
hurrying  up  the  finish,  but  instead  of  obtaining  a 
surface  to  meet  wear,  a  rough  substitute  is  ob- 
tained, uneven  in  surface,  and  far  from  homo- 
geneous, and  the  consequences,  a  series  of  repairs 
to  keep  the  floor  intact. 

On  the  other  hand,  if  the  base  is  allowed  to  set 
for  twelve  to  twenty-four  hours,  all  danger  of 
destroying  the  adhesion  between  the  concrete  and 
steel  has  passed.  The  surface  of  the  base  is  un- 
even, it  may  be  scratched  with  a  rake  to  make 
it  more  uneven,  and  it  should  be  well-wetted 
down  before  applying  the  finish.  With  these 
things  attained,  there  is  no  reason  why  there 
should  not  be  a  sufficient  bond  between  the  base 
and  the  finish.  Then  everything  is  favorable  for 
obtaining  a  level  surface  by  bringing  the  screeds 
to  nails  set  in  the  base  to  exact  grade,  and  the 
men  applying  the  finish  may  have  daylight  by 
which  to  see  what  they  are  doing,  all  of  which 
tend  toward  good  results. 


32      HANDBOOK  ON  REINFORCED  CONCRETE. 

PROTECTING  NEWLY-LAID  WORK. 

Now,  having  obtained  a  floor  surface  properly 
laid  to  take  wear,  the  next  step  in  sequence  seems 
to  be  to  properly  care  for  the  results  already 
obtained  by  protecting  them  from  outside  influ- 
ences. We  have  seen  that,  if  some  portions  of 
the  surface  set  earlier  than  others,  the  result  is 
a  network  of  hair  cracks  dividing  such  surfaces. 
It  is  perfectly  well-known  that  concrete  of  a  given 
mix  requires  a  given  amount  of  water  to  cause 
proper  setting;  any  water  in  excess  will  be  left 
free  to  be  absorbed  by  the  air;  any  deficiency  will 
leave  parts  of  the  concrete  improperly  set.  Along 
this  line  of  reasoning,  it  may  be  easily  seen  that  if 
a  newly-laid  floor  surface  be  left  unprotected  from 
the  sun  on  a  dry,  hot  day,  the  result  will  be  that 
the  rays  of  the  sun,  and  the  surrounding  dry  air 
will  extract  from  the  upper  surface  a  considerable 
amount  of  water.  Being  robbed  of  what  it  should 
require  to  set  properly,  and  at  the  same  time, 
being  forced  in  places  to  set  much  earlier  than 
it  otherwise  would,  it  tends,  by  shrinkage  of  the 
affected  portion,  to  separate  the  same  from  the 
lower  and  less-affected  layers.  The  result  is  im- 
perfect bond  between  the  successive  layers  and 
cracks  between  the  more  or  less  effected  parts  of 
the  exposed  surface,  which,  of  course,  are  detri- 
mental to  wear,  as  well  as  unsightly  in  appearance. 

To  overcome  such  influences,  and  to  hold  nature 
somewhat  in  check,  the  writer  would  suggest  that 


TENSILE    STRENGTH    OF   CEMENT.  33 

just  as  soon  as  an  area,  however  small,  had  re- 
ceived its  final  troweling,  and  had  become  con- 
sistent enough  to  support  a  covering  of  burlap 
or  canvas,  the  same  be  spread  over  the  area  and 
wetted  by  spraying  gently  with  a  hose.  As  the 
surface  below  becomes  harder  and  harder,  water 
should  be  sprayed  over  the  covering  in  increasing 
amounts,  and  just  as  soon  as  the  surface  will 
allow  it,  the  whole  covered  area  should  be  flooded. 
In  about  twenty-four  to  thirty-six  hours,  this 
temporary  covering  may  be  removed,  when  the 
surface  should  be  covered  with  a  layer  of  saw- 
dust or  fine  sand  sufficiently  thick  and  evenly 
distributed  to  protect  all  parts.  Preferably  saw- 
dust should  be  used,  as  the  particles  are  more 
elastic,  and  are  not  so  harsh  upon  the  finished 
surface  when  walked  upon.  Coarse  sand  or  gravel 
should  be  infrequently  resorted  to,  for  upon  areas 
which  require  much  walking  over,  the  surface 
will  become  very  spotted  and  marred,  because 
of  the  coarse  particles  being  pressed  into  the 
surface  not  already  hard.  This  covering  should 
be  flooded  with  water,  and  kept  wet,  or  at  least 
damp,  just  as  long  as  practicable,  or  until  ready 
for  occupancy,  if  possible.  This  covering  not 
only  protects  the  surface  from  atmospheric  influ- 
ences, but  also  from  wear  which  the  newly-made 
surface  could  not  otherwise  withstand.  In  this 
way,  work  upon  or  above  the  newly-placed  area 
may  not  be  delayed  more  than  thirty-six  to 
forty-eight  hours. 


PART    II. 
TENSILE  STRENGTH  OF  CONCRETE-STEEL. 


35 


TENSILE  STRENGTH  OF  CONCRETE 
STEEL,  OR  THE  EFFECT  OF  STEEL 
MEMBERS  UPON  CONCRETE  WHEN 
EMBEDDED  IN  THE  LATTER,  AND 
THE  WHOLE  IS  UNDERGOING  TENSION 
CAUSED  BY  BENDING. 


WHEN  we  come  to  determine  the  tensile  strength 
of  concrete,  when  lying  just  around  or  between 
steel  rods,  as  in  case  of  the  layer  containing  the 
tension  members  near  the  bottom  of  a  concrete- 
steel  beam  undergoing  tension  caused  by  bend- 
ing, we  have  a  more  complicated  problem  to 
deal  with  than  with  the  simple  tensile  strength 
of  a  cement  briquette.  Experiments  galore  have 
shown  just  how  much  may  be  expected  from  a 
tensile  specimen  of  concrete  alone,  when  the  history 
of  its  manufacture  is  known,  and  the  treatment 
it  has  undergone,  and  under  what  conditions.  It 
yet  remains  for  experimenters,  after  many  and 
careful  trials,  to  enlighten  us  concerning  the  in- 
fluence the  steel  members  have  upon  the  concrete 
when  embedded  in  it,  and  the  combination  is 
undergoing  tension  caused  by  bending.  That  this 
influence  is  enormous,  no  one  can  dispute  when 
examples,  and  these  from  reliable  sources  .no 

37 


38        HANDBOOK   ON    REINFORCED    CONCRETE 

doubt,  are  cited,  where  tests  to  destruction  of 
concrete-steel  beams,  by  bending,  have  ruptured 
the  steel  members.  Since  the  ratio  of  the  con- 
crete section  to  the  steel  section  in  the  layer  con- 
taining the  steel  has  not  been  furnished  us,  we 
are  unable  to  compute  the  stress  in  the  concrete 
section,  which,  indeed,  is  to  be  exceedingly  re- 
gretted. We  are,  however,  quite  justified  in  say- 
ing that  in  such  layers,  where,  for  instance,  the 
section  of  the  concrete  between  the  steel  members 
just  equals  that  of  the  steel  itself,  that  the  stress 
in  the  concrete  is  one-tenth  that  in  the  steel, 
allowing  the  ratio  of  the  modulus  of  elasticity  of 
the  concrete  to  steel  to  be  1  to  10. 

As  there  are  several  cases  in  actual  practice 
where  the  equality  of  the  sections  of  steel  and 
concrete  in  the  layer  in  question  actually  exists, 
and  where,  from  the  actual  loading,  the  stress  per 
square  inch  of  steel  figures  15,000,  it  is  but  fair 
to  assume  that  the  stress  caused  in  the  concrete 
thereby  is  one-tenth  of  this,  namely  1,500  pounds 
per  square  inch. 

Critics  who  are  wont  to  call  the  ultimate  tensile 
strength  of  concrete  200  to  300  pounds  per  square 
inch  will  no  doubt  either  laugh  this  reasoning  to 
scorn,  or  will  refuse  to  use  a  construction  which 
imposes  such  exacting  conditions  upon  a  material 
weak  in  itself,  before  stopping  to  consider  that 
we  are  not  dealing  with  the  elements  alone,  but 
with  a  carefully  selected  (or  at  least  it  should  be) 
combination  of  materials.  That  this  combination 


TENSILE   STRENGTH    OF    CONCRETE-STEEL.      39 

has  proved  itself  in  practice  to  be  equal  to  the 
conditions  just  stated  should,  until  experimenters 
have  shown  otherwise,  be  evidence  enough  to 
justify  its  adoption.  How  many  materials  in 
actual  use  of  construction,  and  which  go  appar- 
ently free  from  criticism,  are  there  which  in  them- 
selves are  weak  and  unfit  for  any  use,  but  when  in 
combination  with,  or  constrained  by  other  mem- 
bers, do  excellent  service.  Yet  we  are  just  as 
unable  to  give  this  combination  a  fixed  limit  of 
strength  and  endurance  as  are  we  in  the  case  at 
hand. 

To  determine  a  value  for  this  tensile  strength 
of  concrete  within  the  extreme  fibre,  the  writer 
had  two  test  beams  made  which  were  designed  to 
be  weak  in  concrete-resisting  area  between  the 
steel  members  in  order  to  facilitate  this  method 
of  failure  if  possible.  The  results  and  conclusions 
drawn  from  these  tests  are  given  further  on.  To 
be  sure,  the  manner  of  failure  was  as  anticipated, 
namely  by  tension  in  the  concrete  between  the 
steel  members.  As  may  be  noted  from  the  tests 
at  the  time  of  failure,  the  tensile  stress  in  the 
three  rods  of  Beam  No.  1  was  55,000  pounds  per 
square  inch,  and  in  those  of  Beam  No.  2  at  the 
time  of  failure,  64,000  pounds  per  square  inch. 
From  No.  1  beam,  provided  the  resisting  areas  of 
both  concrete  and  steel  were  equal,  the  tensile 
stress  at  the  time  of  failure  would  have  been  one- 
tenth  of  55,000,  namely  5,500  pounds  per  square 
inch,  but  the  resisting  area  of  the  concrete  was 


40    HANDBOOK  ON  REINFORCED  CONCRETE. 

206  -s-  168  in  excess  over  that  of  the  steel,  which 
would  reduce  the  ultimate  stress  in  the  concrete 
by  the  reciprocal  of  this  ratio,  namely,  to  4,500 
pounds  per  square  inch.  From  the  test  of  No.  2 
beam,  this  value,  by  like  treatment,  becomes 
5,200.  Allowing  a  factor  of  3.5,  which  is  allowed 
in  all  cases,  as  may  be  seen  in  the  explanations  of 
tables,  for  safety,  brings  the  safe  allowable  work- 
ing stress  between  1,000  and  1,500  pounds  per 
square  inch.  From  the  tables,  in  all  cases,  the 
safe-working  stress  of  the  concrete  in  tension  has 
been  kept  between  1,000  and  1,500  pounds  per 
square  inch.  It  is  not  intended  to  assert  that  the 
value  of  the  tensile  strength  of  concrete  can  be 
obtained  from  these  two  experiments.  They  are 
given  merely  to  illustrate  what  may  be  expected, 
and,  as  they  bear  out  common  practice,  they  are 
cited  as  fair  examples  of  the  ordinary  run  of 
experiments,  which  may  be  carried  on  with  the 
object  of  determining  the  tensile  strength  in  view. 

TEST  BEAM  No.  1. 

Duration  of  set 59  days. 

Kind  of  cement  used Portland  Alpha. 

Ratio  of  ingredients 1-2-4. 

Proportion  of  steel      3-f-inch  bars. 

Proportion  of  steel  8-1-inch  U-bars  45°  to  axis 

of  beam. 

Distribution  of  steel f-inch  bars  2£  inches  from 

bottom. 

Distribution  of  steel f-inch  bars,  distances  vary- 
ing from  4  inches  at  ends 
to  12  inches  toward  mid- 
dle. 


TENSILE    STRENGTH    OF    CONCRETE-STEEL.        41 

Manner  of  applying  load    .    .    .     Gradually. 

Application  of  load At  center  of  span. 

One-fourth  load  weighed  on 
scales. 

Deflection  measured  by  micro- 
meter calipers. 

Length  of  beam 10  feet    6  inches. 

Span      10  feet    0  inches. 

Width  of  beam 5  inches. 

Depth  of  beam 15  inches. 

Results  of  Test. 


1 

«j 

"o 

jl 

Deflec- 
tion 
read- 

Aver- 
age 
deflec- 
tion 

Deflec- 
tion 
read- 
ings 
load 

ige  deflec- 
readings 
removed  . 

Total 
set. 

tion  recov- 
>y  removal 
load. 

jrement 
of 
deflection. 

5  deflection 
100  Ibs. 
load. 

1 

o 

c 

ings. 

read- 
ings. 

re- 
moved. 

ill 

3*! 

IF 

Q® 

a  .2 

J3 
"a! 

11 

s 

0. 

.0405 

.0405 

.0405 

488. 

488. 

.0472 

.0471 

.0410 

.0410 

.0005 

.0061 

.0061 

.00125 

.0470 

.0410 

740. 

252. 

.0545 

.0545 

.0424 

.0418 

.0013 

.0127 

.0066 

.00172 

.0546 

.0412 

1140. 

400. 

.0635 

.0635 

.0437 

.0439 

.0034 

.0196 

.0069 

.00172 

.0635 

.0440 

1748. 

608. 

.0678 

.0682 

.0425 

.0425 

.0020 

.0257 

.0061 

.00147 

.0685 

.0425 

2300. 

552. 

.0784 

.0784 

.0450 

.0447 

.0042 

0337 

.0080 

.00147 

.0784 

.0440 

3448. 

1148. 

.1050 

.1050 

.0640 

.0640 

.0235 

.0410 

.0073 

.00119 

.1050 

.0640 

4960. 

1512. 

.1300 

.1297 

.0675 

.0687 

.0282 

.0610 

.0200 

.00123 

.1295 

.0700 

5760. 

800. 

.1530 

.1537 

.0778 

.0778 

.0373 

.0759 

.0149 

.00132 

.1545 

.0778 

6960. 

1200. 

.1820 

.1815 

.0790 

.0788 

.0383 

.1027 

.0268 

.00148 

.1810 

.0785 

8160. 

1200. 

.2145 

.2145 

.0856 

.0857 

.0452 

.1286 

.0259 

.00158 

.2140 

.0858 

42        HANDBOOK    ON    REINFORCED    CONCRETE. 

Failed  under 15,000  pounds. 

Manner  of  failure See  illustration 

Average    elastic    deflection    per    100 

pounds  load 00144. 

1  WL3 
Formula  for  elastic  beam D  =  — 

4o  liiL 

D  =  elastic     deflection     corre- 
sponding to  load  W ' . 
L  =  length  of  span  in  inches. 
E  =  modulus  of  elasticity 
_  Stress  per  square  inch 

Strain  per  inch 

7  =  moment  of  inertia  of  beam 
section  about  neutral 
axis. 

1  X  100  X  1203 
48X1X926 
E  =  modulus      of      elasticity, 

2,640,000. 

Neutral  axis  (when  determined  as  al- 
ready explained)  above  the  under- 
side of  the  beam  • 7.4  inches. 

Or,  below  the  central  axis 1.35  inches. 

Maximum  bending  moment 

=  \  X  15,000  X  120      450,000  inch-pounds. 

Concrete. 
Moment  of  inertia  — 

/  =  (TV  X  5  X  12.53)  +  (5  X  12.5 

X  1.352)  =  926. 
Distance   from   neutral   axis   to   extreme 

fiber  or  layer  in  compression  — 
Y 7.6  inches. 

I   _  9?6 
Y  "  7.6    ' 

Ultimate   compressive   stress  at  extreme 
fiber  or  layer  — 

/  =        '  3,700  Ibs.  sq.  in. 


TENSILE    STRENGTH    OF    CONCRETE-STEEL.         43 


Steel. 
I  —  area  of  section  X  (distance  of  steel  to 

neutral  axis)2  — 
3  X  .56  X  4.92  .........     40.4 

Y  ...............       4.9 

7        40'4 


8  23 


Ultimate  tensile  stress  at  extreme  layer  — 
f  =  450.000  ........... 

8.23 

Ultimate  tensile  stress  of  concrete  within 
this  layer  — 

55,000  X        X  ...... 


4,500  Ibs.  sq.  in., 


10 


, 
6 


modulus  of  elasticity  of  concrete 
modulus  of  elasticity  of  steel 
168       area  .of  steel  in  tensile  layer 
206  =  area  of  concrete  in  tensile  layer 


TEST  BEAM  No.  2. 


Duration  of  set 
Kind  of  cement  used 
Ratio  of  ingredients 
Proportion  of  steel 
Proportion  of  steel 

Distribution  of  steel 
Distribution  of  steel 


Manner  of  applying  load 
Application  of  load  .. 
One  -  twenty  -  fourth 

weighed  on  scales. 
Deflection       measured 

micrometer   calipers. 
Length  of  beam 
Span 

Width  of  beam 
Depth  of  beam 


load 


b 


62  days. 

Portland  Alpha. 

1-2-4. 

3-f  "  bars. 

8-i"   U-bars,  90°   to   axis   of 

beam. 
J-inch  bars,    3£   inches  from 

bottom. 
J-inch  bars,  distances  varying 

from  4   inches  at  ends  to 

12  inches  toward  middle. 
Gradually. 
At  center  of  span. 


10  feet    6  inches. 

10  feet    0  inches. 

5  inches. 

15  inches. 


HANDBOOK    ON    REINFORCED    CONCRETE. 


Results  of  Test. 


•c 

5 

"o 

c  . 

Deflec- 

Aver- 
age 

Deflec- 
tion 

it! 

1*1 

ent 
ection. 

c 
o 

11 

Total  Ic 

Increme 
load 

tion 
read- 
ings. 

deflec- 
tion 
read- 
ings. 

read-* 
ings 
load 
re- 
moved. 

Average  c 
tion  reac 
load  remi 

Total 

set. 

Defied 
recovere 
removal  oi 

fi   53 

jfS-S 

§  .s 

~  1 
* 

111 
If 

W 

0. 

.2714 

.2714 

.2714 

960. 

960. 

.2883 

.2884 

.2714 

.2714 

.0000 

.0170 

.0170 

.00177 

.2884 

.2714 

2230. 

1270. 

.3304 

.3304 

.2868 

.2872 

.0158 

.0432 

.0262 

.00194 

.3305 

.2880 

2810. 

580. 

.3435 

.3437 

.2740 

.2733 

.0019 

.0704 

.0272 

.00251 

.3440 

.2725 

3650. 

840. 

.3548 

.3574 

.2795 

.2783 

.0069 

.0791 

.0087 

.00217 

.3600 

.2770 

4800'. 

1150. 

.3815 

.3817 

.2895 

.  2880 

.0166 

.  0937 

.0146 

.00195 

.3820 

.2865 

5040. 

240. 

.4010 

.4010 

.2950 

.2045 

.0231 

.1065 

.0128 

00212 

.4010 

.2940 

5930. 

890. 

.4190 

.4195 

.2960 

2945 

.0000 

.1250 

.0195 

.00211 

.4200 

.2930 

Failed  under 16,200  Ibs. 

Manner  of  failure See  illustration 

Average  elastic  deflection  per  100  Ibs.  load    .00208. 


.00208 


100  X  1203 
48  X  E  X  732 


;  whence 


E  =  modulus  of  elasticity 

Neutral  axis  (above  underside  of  beam) 
Neutral  axis  (below  central  axis)  .  .  . 
Maximum  bending  moment 


2,420,000. 

7.95  inches. 
1.30  inches. 


X  16,000  X  120 


480,000  in.-lbs. 


TENSILE   STRENGTH   OF   CONCRETE-STEEL.      45 


CUT  SHOWING  FAILURE  OF  BEAM  No.  1. 


CUT  SHOWING  FAILURE  OF  BEAM  No.  2. 


46   HANDBOOK  ON  REINFORCED  CONCRETE. 

Concrete. 
Moment  of  inertia  — 

/  =  (rV  X  5  X  11.53)  +  (5  X  11.5 

X  1.302)      732. 

Y 7.05  inches. 

7   -  732  104 

Y  ~  7M> 

Ultimate  compressive  stress  at  extreme 
layer  — 

480,000 
/  =      ^4        4610  Ibs.  sq.  in. 

Steel. 

I  =  3  X  56  X  4.452      t    .     33.4. 

Y 4.45. 

Y      7.5. 

Ultimate  tensile  stress  at  extreme  layer  — 

,=™ 64,000  lb,sq.  in. 

/  .£> 

Ultimate  tensile  stress  of  concrete  within 
this  layer  — 

=  64,000  X  -^  X  i5| 5;200  Ibs.  sq.  in. 

AU          ^Uo 

REMARKS  CONCERNING  TESTS  No.  1  AND  No.  2. 

These  tests  were  carried  out,  as  the  cuts  will 
clearly  illustrate,  by  applying  a  central  load  at 
the  center  of  the  span  by  means  of  a  screw-jack, 
and  determining  same  by  means  of  allowing  a 
portion  of  same  to  be  weighed  upon  a  set  of  scales. 
The  deflection  readings  were  obtained  by  fixing  a 
pair  of  micrometer  calipers  to  the  beams  at  the 
center  of  the  span,  and  by  taking  successive  read- 


TENSILE    STRENGTH   OF   CONCRETE-STEEL.      47 

ings  when  the  screw  of  same  just  came  into  con- 
tact with  a  steel  piano  wire  stretched  across  pins 
set  into  the  ends  of  the  beam  at  the  neutral  axis, 
and  directly  over  the  supports.  The  contact  was 
determined  more  closely  by  allowing  the  microm- 
eter screw  to  make  an  electric  circuit  through  the 
piano  wire,  two  dry  cells,  and  an  induction  ringer. 


CUT  SHOWING  ARRANGEMENT  OF  APPARATUS  FOR  CONDUCTING  TESTS 
No.  1  AND  No.  2. 


All  readings  were  checked  by  two  individuals  to 
.0005  or  .0010  of  an  inch. 

It  will  be  noted  that  in  working  up  the  results, 
no  attention  was  paid  to  the  concrete  below  the 
tension  layer  of  steel,  and  hence  in  Beam  No.  1 
the  effective  depth  was  12.5  inches,  while  in  Beam 


48         HANDBOOK   ON    REINFORCED    CONCRETE. 

No.  2  only  11.5  inches,  instead  of  the  nominal 
depth  of  15  inches  as  given. 

As  before  stated,  these  beams  were  designed  to 
be  weak  in  concrete-resisting  area  in  the  tensile 
layer  between  the  steel,  expecting  this  manner  of 
failure.  In  one  case  it  was  clearly  marked,  and 
in  the  other,  the  first  indications  were  tending  in 
this  direction,  but  which  ultimately  developed  in- 
to a  shear-crack,  the  failure  being  a  compromise 
between  the  two. 

CONCLUSIONS  CONCERNING  TESTS. 

It  may  be  observed,  by  referring  to  the  sets  of 
deflection  readings  given,  that  like  successive  in- 
crements of  load  did  not  produce  like  increments 
of  deflection.  On  the  other  hand,  each  successive 
like  increment  of  load  produced  a  deflection  10 
to  30  per  cent  in  excess  over  the  preceding  incre- 
ment of  deflection. 


RESULTS    OF   TESTS. 


49 


Floor  Test  No.  1. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec-» 
tion  per 
100  \b3.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

1A 

Sq.  ft. 
36.5 
137 

Inches. 
.0310 
1638 

Sq.  ft. 
.0850 
1195 

Inches. 

Inches. 

Inches. 

249. 

.2412 

.0969 

249. 

.3700 

.1484 

1A-1B 

280. 

Lin.  ft. 
822.5 

.4607 

Inches. 
.0780 

.1648 

Lin.  ft. 
.0095 

.4688 

.3438 

.1250 

3170. 

.0938 

.0296 

4365. 

.1300 

0298 

4365. 

.1720 

.0394 

IB 

5600. 

Sq.  ft. 
63.7 

.2750 

Inches. 
.0360 

.0492 

Sq.  ft. 
0390 

.2750 

.2230 

.0520 

249. 
312. 

.1260 
1585 

.0506 
0509 



312. 

.2065 

.0662 

1B-1C 

420. 

Lin.  ft. 
1265 

.4888 

Inches. 
0620 

.1165 

Lin.  ft. 
0049 

.5900 

.3340 

.2560 

3713. 

.0940 

.0025 

4635. 

.1300 

.0028 

1C 

4635. 
6300. 

Sq.  ft. 
125 

.1700 
.2800 

Inches. 
0522 

0037 
.0045 

Sq.  ft. 
0418 

.2800 

.1300 

.1500 

245. 

.1175 

0480 

303. 

.1475 

.0488 

303 

.2125 

.0702 

420. 

.4950 

.1180 

.5900 

.3560 

.2340 

50        HANDBOOK    ON    REINFORCED    CONCRETE. 


Floor  Test  No.  2. 


1 

2 

3 

4 

5 

6 

7 

Mean 

increment 

Loca- 
tion 

in 

Total 
load. 

Mean 
deflec- 

deflec- 
tion per 
100  Ibs.  per 

Greatest 
deflec- 

Amount 
deflec- 
tion 

Perma- 
nent 

section. 

tion. 

sq.  ft.  or 
per  1000 

tion. 

recov- 
ered. 

set. 

Ibs. 

lin.  ft. 

2C 

Sq.  ft. 
205 

Inches. 
1190 

Sq.  ft. 
0580 

Inches. 

Inches. 

Inches. 

OCA 

1428 

0571 

ocn 

1962 

0785 

250. 

.2241 

.0898 

.2450 

.2031 

.0419 

1C-2C 

Lin.  ft. 
9ORO 

Inches. 
0469 

Lki.  ft. 
0228 

2500 

0780 

0313 

9K.OO 

0780 

0313 

2^00 

0780 

0313 

0780 

2C-3C 

Lin.  ft. 

Inches. 

Lin.  ft, 

2060 

Oil 

0053 

ornn 

033 

0132 

2500 

2500. 

.035 

.0140 

.0700 



2C-2B 

Sq.  ft. 

Inches 

Sq.  ft. 

125 

080 

0640 

125 

080 

0640 

125 

094 

0753 

125. 

.125 

.1000 

.1250 



Floor  Test  No.  3. 


3C 

Sq.  ft. 

Inches. 
032 

Sq.  ft. 

057 

250 

248 

0835 

250. 

.255 

.1020 

.2550 

.2550 

.0000 

51 


Floor  Tests  No.  3.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

3C-4C 

Lin.  ft. 
1500 

Inches. 
.046 

Lin.  ft. 
.0370 

Inches. 

Inches. 

Inches. 

1500. 
1500 

.062 
078 

.0414 
0520 

2500. 

.078 

.0312 

3750. 

.094 

.0251 

3O3B 

5000. 
Sq.  ft. 
1250 

.209 
Inches 
.120 

.0418 
Sq.  ft. 
.0960 

.2090 

.1630 

.0460 

1250. 

.125 

.1000 

.1250 

.1250 

.0000 

Floor  Test  No.  4. 


4C 

Sq.  ft. 
1250 

Inches. 
.1075 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

2500. 

.1938 

2500. 

.2250 

4C-5C 

2500. 

Lin.  ft. 
1250. 

.0150 

.2700 

.2550 

.0150 

1250. 

.0400 

5000. 

.1500 

5000. 

.1700 

2500. 

.1700 

4C-4B 

Sq.  ft. 
60. 

.0320 

125. 

.0900 

125. 

.0480 

125. 

.0650 

.0900 

52 


HANDBOOK   ON    REINFORCED    CONCRETE. 


Floor  Test  No.  5. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

5C 

Sq.  ft. 
250. 

Inches. 
.2500 

Sq.  ft. 
.1030 

Inches. 

Inches. 

Inches. 

250. 

.2500 

.  1030 

250. 
250 

.2812 
3200 

.1200 
1280 

250. 

2187 

250. 

.1900 

.3180 

.3180 

.000 

5C-6C 

Lin.  ft. 

Lin.  ft. 

2500. 
2500 

.010 
032 

.0040 
0128 

3750. 
5000 

.062 
095 

.0165 
0190 

5000. 

.218 

.0436 

5000. 

.156 

.0312 

2500. 

.010 

.0400 

.2180 

.1830 

.035 

5C-5B 

Sq.  ft. 
125 

050 

Sq.  ft. 
040 

125. 
125 

.093 
130 

.0743 
1041 

125 

124 

0991 

125 

069 

125. 

.050 

.  1300 

.1300 

.000 

RESULTS   OP    TESTS. 
Floor  Test  No.  6. 


53 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

6C 

Sq.  ft. 
125 

Inches. 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

250. 
250 

.2180 
2300 



250 

2530 

250. 

.2480 

6C-7C 

250. 
Lin.  ft. 
2500 

.2300 
1250 

.3250 

.2550 

.0700 

2500 

.  1  250 

5000 

2750 

5000 

1900 

5000. 

.1600 

5000 

2450 

2500 

.1950 

.2450 

.0890 

1560 

6C-6B 

Sq.  ft. 
62 

0310 

125. 

.0650 

125 

125. 

0940 

125 

1000 

125. 

.1000 

.1000 

.0000 

Floor  Test  No.  7. 


7C 

Sq.  ft. 
125 

Inches. 
1000 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

250 

2200 

250 

250 

2812 

250 

2812 

250. 

250. 

.2770 

.2812 

.1512 

.1300 

54          HANDBOOK    ON    REINFORCED    CONCRETE. 
Floor  Test  No.  7.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

7C-8C 

Lin.  ft. 
1250. 

Inches. 
.0570 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

2500 

0900 

2500. 

.0980 

2500 

1200 

3750. 

.1562 

5000. 
5000 

.1900 
1500 

7C-7B 

2500. 
Sq.  ft. 
62  0 

.1600 
.1150 

.1900 

.1330 

.0570 

125. 
125 

.1300 
1900 

125. 

.1800 

125. 

.1900 

125 

1850 

125. 

.1900 

.0400 

.1500 

Floor  Test  No.  8. 


80 

Sq.  ft. 
125. 
250. 

Inches. 
.0500 
2750 

Sq.  ft. 
.0560 
.1025 

Inches. 

Inches. 

Inches. 

8C-9C 

250. 
250. 
Lin.  ft. 
1825 

.3075 
0310 

.1230 
Lin.  ft. 
0169 

.3075 

.1875 

.1200 

5000. 

.1560 

0276 

5000. 
5000. 

.2300 
.3700 

.0460 
.0740 

8C-8B 

2500. 
Sq.  ft. 
62. 

.2700 
.092 

Sq.  ft. 
148 

.3700 

.2175 

.1525 

125. 
125. 

.3125 
3075 

.250 
246 

125. 

.3125 

.0650 

.2475 

RESULTS    OF    TESTS. 


55 


Floor  Test  No.  9. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

9C 

Sq.  ft. 
62. 
250 

Inches, 
.093 
234 

Sq.  ft. 
.150 
094 

Inches. 

Inches  . 

Inches  . 

250 

247 

098 

250 

345 

138 

9C-10C 

250. 

Lin.  ft. 
620 

.329 
015 

.132 

Lin.  ft. 
024 

.345 

.160 

.185 

2500 

030 

012 

5000 

129 

0258 

5000 

281 

9C-9B 

5000. 

Sq.  ft. 
31 

.219 
063 

.0438 

Sq.  ft. 
201 

.219 

.074 

.145 

125 

205 

164 

125 

234 

187 

125 

313 

250 

125. 

.290 

.232 

.313 

.037 

.276 

Floor  Test  No.  10. 

IOC 

Sq.  ft. 

Inches  . 

Sq.  ft. 

Inches. 

Inches  . 

Inches  . 

125 

189 

1514 

250 

380 

1520 

250. 

.370 

.1480 

.3800 

.0675 

.3125 

56        HANDBOOK   ON    REINFORCED    CONCRETE. 


Floor  Test  No.   10. —Continued. 


1 

2 

3 

4 

5 

6 

7 

Mean 

increment 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

Ibs. 

lin.  ft. 

10C-11C 

I  An.  ft. 

Inches. 

Lin.  ft. 

Inches. 

Inches. 

Inches. 

2500 

2500. 

.375 

0750 

2500. 

.406 

.0810 



2500. 

.348 

.1394 

.4060 

.1270 

.2790 

10C-10B 

Sq.  ft. 

Sq.  ft. 

• 

62. 

.156 

252 

125. 

.284 

.227 

125. 

.268 

.214 

.2840 

.0000 

.2840 

Floor  Test  No.  11. 


11C 

Sq.  ft. 

Inches. 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

125. 

.1175 

.0940 

250. 

.4375 

.175 

250. 

.4688 

1876 

250. 

.5600 

.2220 

.5600 

.1200 

.4400 

11C-12C 

Lin.  ft. 

Lin.  ft. 

1250. 

.1875 

.150 

2500 

2188 

0877 

3750 

3080 

0821 

5000. 

.4640 

.0926 

.4640 

.0340 

.4300 

11C-11B 

Sq.  ft. 

Sq.  ft. 

62 

2790 

455 

125 

3280 

263 

125 

4040 

324 

125. 

.4970 

.397 

.4970 

.0000 

.4970 

RESULTS    OF    TESTS. 


57 


Floor  Test  No.  12. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 

deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

12C 

Sq.  ft. 

Inches. 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

125. 

.2180 

.1742 

250. 

.5050 

.2020 

.5050 

.1925 

.3125 

12C-13C 

Lin.  ft. 
2500 

0660 

Lin.  ft. 
0264 

5000. 

.4690 

.0938 

.4690 

.0940 

.3750 

12C-I2B 

Sq.  ft. 

Sq.  ft. 

62. 

.0940 

.1516 

125. 

.3780 

.3022 

.3870 

.0795 

.3075 

Floor  Test  No.  13. 


13C 

Sq.  ft. 

Inches. 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

125. 

.1230 

.0984 

250. 

.5800 

.2320 

.5800 

.2360 

.3440 

13C-14C 

Lin.  ft. 

Lin.  ft. 

1250 

1510 

1210 

5000. 

.5780 

.1158 

2500. 

.5630 

.5780 

.2950 

.2830 

13C-13B 

Sq.  ft. 

Sq.  ft. 

62 

0625 

1010 

125. 

.4687 

.3760 

.4687 

.0987 

.3700 

58        HANDBOOK    ON    REINFORCED   CONCRETE. 


Results  of  Tests. 


1 

2 

3 

4 

No.  of  bays. 

Location 
in  bay. 

Average  of 
greatest 
deflection. 

Average  of 
least 
deflection. 

S£ 

03  C 
fe« 

<C 
O 

Average 
greatest 
deflection 
recovered. 

Average 
least 
deflection 
recovered. 

IB,  1C,  20,  30,  40, 
50,60,70,80,90, 
100. 

Center  250 
Ibs  sq.  ft. 

.3117 

1A    110,  120,  130 

Center  250 
Ibs.  sq.  ft. 

5160 

Average. 

.4139 

1A,  1C,  20,  30,  4C, 
50,  6C,  and  130, 

Center  250 
Ibs.  sq.  ft. 

.2552 

IB,  70,  8J,  90,  110, 
and  120. 

Center  250 
Ibs.  sq.  ft. 

.1687 

Average. 

30-40,  1A-1B,  40- 

50,  5C-6C,  8C-9C, 
130  140. 

Girder  5000 
Ibs.  lin   ft. 

2046 

1B-1C,  6C-7C,  7C- 
80,  9C-10C,  100- 
110   120  130 

Girder  5000 
Ibs.  lin.  ft 

.1034 

3C-3B,  5C-5B,   60- 
6B   130  13B 

Side  125  Ibs. 
sq.  ft. 

1134 

7C-7B,  8C-8B,  90- 
9B   100  10B 

.0554 

Average 

RESULTS   OF   TESTS. 
Results  of  Tests.  — Continued. 


59 


li 

0>  83 

32 

O 

5 

6 

.« 

W>T3 
2  0 
Q;  ^ 

<z 

O 

7 

8 

E 

Average 
of 
7  and  8. 

E 

Average 
of 
column 
6. 

Ratio        Ratio 
WL3         WLS 
DEI         DEI 
from  3      from  4 
Calling  E  = 
3,000,000. 

E  from  5 

calling 
WL*         5 
DEI  ~  384 

E  from  6 
calling 
JFL3         5 

DEI  ~384 

, 

2,060,000 

112 

1 

1,375,000 

.2120 

168 

1 

1,650,000 

140 

1 

5,590,000 

41.2 

1 

2,820,000 

.1540 

81.7 

1 

3,750,000 

61.5 

"127 

1,820,000 

1 
"260 

888,000 

.0844 

1 

1,190,000 

2,197,000 

194 

60      HANDBOOK  ON  REINFORCED  CONCRETE 

REMARKS  CONCERNING  FLOOR  TESTS, 

These  tests  were  carried  out  upon  a  floor  com- 
posed of  20-foot  square  bays,  a  SJ-inch  floor, 

5  X  12-inch  beams,  18  feet  10  inches  long  between 
girders,   and    spaced    3-feet    5-inch   centers,    and 
14  X  24-inch  girders,  clear  span  18  feet  2  inches, 
all  of  concrete  reinforced  by  steel  rods.     This  floor 
had  been  erected  eight  months  previous  to    the 
time  of  testing,  having  withstood  in  the  mean- 
time   the    effects    of    a    severe    winter,   although 
protected  as  well  as  could  be.     The  load  consist- 
ing of  sand  bags,  was  uniformly  distributed,  and 
covered  three  consecutive  bays  at  once  in  order 
to  obtain  the  full  loading  over  the  center  bay,  and 
the  girders  on  either  side  supporting  same. 

The  loads  given  under  column  2  are  In  addition 
to  the  weight  of  the  floor  itself. 

Deflection  readings  were  taken  both  by  an 
engineers'  level  and  by  a  multiplying  lever,  which 
recorded  four  times  the  actual  deflection.  The 
items  entered  under  column  3  are  the  means  of 
the  deflection  taken  by  both  methods.  Column  5 
gives  the  greatest  deflection  resulting  from  the 
greatest  loading  recorded  under  column  2.  Column 

6  shows  the  amount  of  deflection  recovered  upon 
the  removal  of  all  the  live  loading.     This  repre- 
sents the  elastic  deflection,  and  is  the  measure  of 
the  elasticity  of  the  floor  from  which  the  modulus 
of  elasticity,  given  under  "Results  of  Tests/7  was 
computed. 


RESULTS   OF   TESTS.  61 

Floor  Test  No.  86.  —  Time  of  Set,  8  Months. 


1 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

8B 

Sq.  ft. 

Inches. 

Sq.  ft. 

Inches. 

Inches. 

Inches. 

200. 
385. 

.2188 
.3750 

.1094 
.0975 

400. 

.4055 

.1014 

.4055 

.3375 

.0680 

8B-8C 

Sq.  ft. 
100. 

.1250 

Sq.  ft. 
.1250 

193 

2530 

1311 

200. 

.2570 

.1285 

.2570 

.1640 

.0930 

7B-8B 

Lin.  ft. 
2000. 

.0314 

Lin.  ft. 
.0157 

3650 

0625 

0171 

4000. 

.1200 

.0300 

.1200 

.0650 

.0550 

8A-8B 

Sq.  ft. 
100. 

.0910 

Sq.  ft. 
.0910 

193 

1850 

0960 

200. 

.2100 

.1050 

.2100 

.1760 

.0340 

8B-9B 

Lin.  ft. 
2000. 

.0310 

Lin.  ft. 
.0155 

3650 

0660 

0181 

4000. 

.0890 

.0223 

.0890 

.0740 

.0150 

62        HANDBOOK   ON   REINFORCED    CONCRETE. 
Floor  Test  No.  14. 


1 

2. 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set. 

14C 

Sq.  ft. 
60 

Inches. 
1250 

Sq.  ft. 
2090 

Inches. 

Inches. 

Inches. 

150 

2500 

1670 

175 

4063 

2320 

200 

5938 

2969 

210 

6563 

3130 

220 

7188 

3270 

235 

8750 

3730 

250 

1  0000 

4000 

13C-14C 

250. 

Lin.  ft. 
2500. 

1.0780 
.1250 

.4320 
Lin.  ft. 

1  .  0780 
.1250 

.5467 
.0940 

.5313 
.0310 

14C-14B 

Lin.  ft. 
2500 

1300 

1300 

.1010 

0290 

14C-15C 

Lin.  ft. 
2500 

.3700 

.3700 

.2100 

.1600 

14C-14D 

Lin.  ft. 
2500. 

.2813 

.2813 

.1563 

.1250 

Time  of  set,  17  days. 

14C  represents  8-inch  flat  slab,  20-foot  0-inch  span  each 
way. 

13C-14C  represents.  14  X  24-inch  girder,  20-foot  0-inch 
span. 

14C-14B  represents  14  X  24-inch  girder,  20-foot  0-inch  span. 

14C-15C  represents  22  X  8-inch  girder.  20-foot  0-inch  span. 

14C-14D  represents  22  X  8-inch  girder,  20-foot  0-inch, 
s^an. 

NOTE.  —  Cracks  developed  diagonally  across  flat  slab 
under  175  pounds  square  foot.  Opened  badly  at  end  of  test. 


RESULTS   OF   TESTS. 
Roof  Test  No.  22.  —  Time  of  Set,  14 


63 


Days. 


t 

2 

3 

4 

5 

6 

7 

Loca- 
tion 
in 
section. 

Total 
load. 

Mean 
deflec- 
tion. 

Mean 
increment 
deflec- 
tion per 
100  Ibs.  per 
sq.  ft.  or 
per  1000 
Ibs. 
lin.  ft. 

Greatest 
deflec- 
tion. 

Amount 
deflec- 
tion 
recov- 
ered. 

Perma- 
nent 
set 

21A-22A 

Lin.  ft. 
1250. 

Inches. 
.0000 

Inches. 

Inches. 

Inches. 

1100. 

0000 

0000 

0000 

0000 

22A 

Sq.  ft. 
62.5 

.1860 

Sq.  ft. 
2980 

55.0 

.1235 

.2250 

.1860 

.1225 

.0625 

22A-23A 

Lin.  ft. 
1250. 

.0000 

Lin.  ft. 

1100. 

.0000 

.0000 

.0000 

.0000 

21C-22C 

Lin.  ft. 

1250. 

.0000 

.0000 

.0000 

.0000 

22C 

Sq.  ft. 

Sq.  ft. 

62.5 

.0700 

.1120 

.0700 

.0700 

.0000 

22C-23C 

Lin.  ft. 
1250. 

0000 

0000 

0000 

0000 

The  roof  was  composed  of  a  20-foot  square  bay,  1\  inches 
thick,  carried  by  2.5  X  12-inch  beams,  19-foot  4-inch  span, 
spaced  3-foot  2-inch  centers,  which,  in  turn,  were  carried 
by  8  X  24-inch  girders,  19-foot  0-inch  clear  span. 


64         HANDBOOK    ON    REINFORCED    CONCRETE. 

REMARKS  UPON  PLOTS. 

The  following  three  plots  are  inserted  to  show 
the  results  of  various  tests  taken  to  determine  the 
effect  of  temperature  upon  reinforced  concrete  as 
regards  expansion  and  contraction.  The  first  gives 
the  change  in  length  of  a  section  of  floor  fifty  feet 
long  for  corresponding  changes  of  temperature. 
The  second  plot  gives  the  change  in  thirty  feet, 
while  the  third  is  a  combination  of  the  two  re- 
duced to  a  section  ten  feet  long. 

At  first  glance  the  results  may  seem  to  vary 
greatly  from  the  mean  or  from  the  curves  drawn 
to  represent  the  relationship  between  expansion 
and  temperature.  This  is  due  to  plotting  the 
ordinates  to  a  large  scale,  which  shows  up  the 
irregularities  to  a  great  extent  in  the  first  two 
plots.  However,  when  these  are  reduced  to  Plot  3, 
the  curves  drawn  are  seen  to  f&irly  represent  the 
average  relationship  desired. 

The  curves  shown  by  full  lines  were  plotted 
between  points  o,  o,  and  the  average  abscissas, 
and  ordinates  taken  from  the  tables  shown  on 
Plots  1  and  2,  which  give  the  extreme  changes. 
On  the  other  hand,  the  curves  shown  by  broken 
lines  give  the  average  results  of  the  tests. 

The  method  of  carrying  on  these  tests  was  as 
follows:  A  set-up  point  was  located,  so  that  it 
could  be  produced  at  any  time.  From  this  point 
a  transit  line  was  produced  upon  the  corner 
column  of  a  building  between  the  ground  and  the 


COEFFICIENT    OF    EXPANSION. 


65 


Expansion  in  feet. 


66        HANDBOOK   ON    REINFORCED    CONCRETE. 

underside  of  the  first  floor,  and  the  same  scratched 
in  with  a  fine  line  by  a  knife.  At  the  same  time 
the  temperature  was  taken  of  the  atmosphere  in 
the  vicinity  of  the  first  floor,  and  also  of  the 
ground  near  the  base  of  the  column.  These  tem- 
peratures were  assumed  to  be  the  temperatures  of 
the  first  floor  and  of  the  column  footing  respec- 
tively. Since  these  tests  were  not  taken  immedi- 
ately after  a  sudden  change  of  temperature,  the 
concrete  of  the  first  floor  had  time  in  all  cases  to 
assume  the  outside  temperature  as  nearly  as  might 
be,  and  hence,  the  assumption  just  made  cannot 
be  far  from  the  true  values. 

To  make  a  test,  the  same  transit  was  accurately 
set  up  over  the  point  already  determined,  a  fore- 
sight was  taken  at  either  the  top  or  bottom  ex- 
tremity of  the  knife  scratch,  and  the  line  produced 
at  the  other  extremity  of  the  scratch,  and  any 
difference  between  the  new  and  original  lines 
noted.  At  the  same  time  temperatures  were 
taken  both  of  the  outside  atmosphere  and  of  the 
ground.  From  these  the  change  of  temperature 
between  the  first  floor  and  the  column  footing 
could  be  determined,  and  this  change  of  tempera- 
ture resulted  in  a  change  of  length  of  the  first 
floor,  as  just  determined  by  the  difference  between 
the  new  and  original  lines. 

These  tests  were  carried  on  at  a  time  of  the  year 
when  the  variation  of  the  temperature  of  the 
ground  was  very  slight,  and  could  have  been 
neglected  without  affecting  the  value  of  the  tests 


COEFFICIENT   OF   EXPANSION. 

Expansion  in  Feet 


67 


O 


Q. 
(D 
(IP 


j 

1 

• 

1 

1 

1 

i 

C 

C 

> 

i 

0 
M 

E 

st 

\s 

YL 

V 

\ 

\\ 

< 

j 

:  c 

3 

I 

\ 

§ 

* 

10      K 

>  — 

c 

i| 

m 

D   - 

f 

\ 

\ 

\ 

\ 

4^ 

^ 

•*"      4 

•  ^ 

1 

=  = 

C 

\ 

i 

\ 

- 

~n 

3 

-  r 

T 

\ 

\ 

C 

1-- 

: 

' 

r 

n 

o 

\ 

"•c 

n  > 

< 

\ 

s 

g 

g 

§c 

3     O 

i 

^ 

\ 

CP 

0 

« 

)      VO 

\ 

\ 

} 

. 

- 

i 

n  ^ 

i 

\ 

^ 

? 

«  . 

; 

\ 

\ 

\ 

1 

7 

* 

V 

\ 

o. 

\, 

o 

\ 

j 

M 

^ 

^ 

c 

^  ' 

. 

\ 

^ 

G 

\ 

1 

0 

\ 

[ 

o 

^ 

\ 

* 

0 

\ 

Y 

£. 

0 

V 

'•^ 

\ 

V- 

0 

'    * 

k 

v 

y 

t^ 

\ 

> 

^> 

^5> 

• 

0 

y 

_\j^ 

y 

ij 

1 

r. 

V 

*, 

\^i 

^ 

V^ 

V* 

Y- 

^ 

•p 

•3 

, 

'A 

^ 

\ 

i  f 

0 

r 

V 

c 

j 

68         HANDBOOK   ON   REINFORCED   CONCRETE. 

to  any  extent,  because  the  base  of  the  column,  the 
footing  of  same,  and  the  curtain  walls  between 
this  column  footing  and  its  neighbors,  were  sur- 
rounded by  frozen  earth  and  ice.  However,  any 
slight  variation,  when  it  was  known  not  to  be  in 
error,  was  allowed  for. 

Readings  were  taken  on  the  four  corner  columns, 
and  in  both  directions,  namely,  east-west  and 
north-south,  on  each  of  the  four  columns.  This 
required  eight  set-ups.  The  building  in  question 
had  an  expansion  joint  fifty  feet  from  the  ends  in 
a  north-south  direction,  and  was  sixty  feet  wide, 
thus  allowing  a  length  for  expansion  in  an  east- 
west  direction  of  thirty  feet  for  each  of  the  two 
corner  columns  at  either  end. 

CONCLUSIONS. 

By  referring  to  the  combined  plot,  it  may  be 
seen  that  the  data  contained  there  is*  sufficient  to 
determine  the  coefficient  of  expansion.  Take  the 
point,  for  instance,  whose  coordinates  are  42.5, 
.0029.  This  means  that  for  a  change  in  tempera- 
ture of  42.5°,  there  was  a  corresponding  change 
in  length  of  .0029  feet  per  ten  feet,  or  .00029  feet 
per  one  foot.  The  corresponding  change  in  length 
per  one  degree  may  be  represented  by  the  ex- 
pression .00029  -&-  42.5  equals  .00000682,  which  is 
the  coefficient  of  expansion.  By  using  the  point 
whose  coordinates  are  42.5,  .0026,  the  resulting 
coefficient  of  expansion  becomes  .00000601.  The 


COEFFICIENT   OF    EXPANSION.  69 

og  b   Expansion  in  Feet 


70    HANDBOOK  ON  REINFORCED  CONCRETE. 

mean  of  the  two  is  .00000642,  and  this  value  is 
used  in  the  following. 

In  temperate  climates  a  change  of  temperature 
of  70°  F.  may  be  considered  a  maximum  either 
way  from  the  temperature  under  which  the  origi- 
nal setting  ordinarily  takes  place.  This  change 
would  cause  a  strain  of  .00000642  X  70  =  .000448 
inches  in  the  concrete,  and,  since  the  coefficient  of 
expansion  of  steel  is  .00000657,  the  strain  in  the 
steel  would  be  .000459  inches,  or  practically  the 
same  as  that  in  the  concrete.  This  strain  causes 
a  stress  of  13,780  pounds  per  square  inch  in  the 
steel,  calling  the  modulus  of  elasticity  30,000,000. 

To  determine  the  percentage  of  metal  required 
for  a  change  of  70°  when  there  is  developed  in  the 
steel  a  stress  not  greater  than  the  elastic  limit, 
which  may  be  considered  52,000  pounds  per  square 
inch  with  a  high  carbon  steel,  we  may  proceed  as 
follows:  The  amount  of  stress  which  may  be 
brought  to  bear  upon  the  steel  by  the  concrete, 
when  the  same  has  reached  its  ultimate  tensile 
stress,  =  52,000  -  13,780  =  38,220  pounds  per 
square  inch.  The  ultimate  tensile  stress  of  the 
concrete  may  be  considered  to  be  300  pounds  per 
square  inch.  Hence  the  remaining  stress  of 
38,220  pounds  per  square  inch  would  resist  the 
stress  of  38,220  -5-  300  =  127  square  inches  of  con- 
crete stressed  to  300  pounds  per  square  inch. 

In  order  to  develop  the  ultimate  stress  in  a 
square  foot  section  of  concrete  would  require  a 
section  of  steel  that  would  resist  the  stress  of 


COEFFICIENT   OF    EXPANSION.  71 

72  square  inch  concrete  after  the  same  hag 
reached  its  ultimate  tensile  stress.  Under  this 
condition  the  steel  section  would  offer  half  the 
resistance  to  elongation,  while  the  concrete  would 
offer  the  other  half,  and  the  square  foot  section, 
which  might  be  treated  as  72  square  inches  of 
concrete  and  its  equal  of  steel,  each  stressed  to 
its  elastic  limit,  or  as  144  square  inches  of  con- 
crete stressed  to  300  pounds  per  square  inch,  its 
ultimate  tensile  stress.  Consequently,  since  1 
square  inch  of  steel  stressed  to  52,000  pounds  per 
square  inch  is  equivalent  to  127  square  inches 
of  concrete  stressed  to  300  pounds  per  square 
inch  in  tension,  to  care  for  one  square  foot  of 
concrete,  considered  as  72  square  inches  of  con- 
crete and  its  equivalent  of  steel,  would  require 
72  -*•  127  =  .57  or  practically  .6  square  inches  of 
steel. 


PAET    III. 
DESIGNS  OF  CONCRETE  STRUCTURES. 


73 


TABLE  I. 


DESCRIPTION  OF  TABLE  I. 

IN  using  Table  I,  all  that  is  required  to  be 
known,  in  order  to  design  the  beam  or  girder,  is 
the  maximum  bending  moment.  When  this  is 
known,  either  in  inch-pounds  or  foot-pounds,  pick 
out  the  next  larger  value  in  column  5,  if  in  inch- 
pounds,  or  in  column  6,  if  in  foot-pounds,  pro- 
vided the  designer  will  accept  a  factor  of  safety 
of  3.5  as  ample;  if  not;  use  columns  7  or  8  in  a 
like  manner,  which  allow  for  a  factor  of  safety  of 
5.  From  the  location  of  the  proper  moment  to 
fit  the  case  at  hand,  by  following  horizontally  to 
the  left,  column  1  will  give  the  size  of  beam  as 
far  as  concrete  is  concerned.  This  size  includes 
the  concrete  protection  below  the  steel  tension 
members  and  the  base  of  the  floor,  but  does  not 
allow  for  the  top  1-inch  finish.  In  other  words, 
the  depth  of  the  beam  given  in  column  1,  which 
in  all  cases  is  the  second  of  the  two  dimensions, 
takes  into  account  the  entire  depth  save  1  inch, 
which  is  to  be  added  to  the  top  of  floor  for  wear. 

Column  5  gives  the  total  moment  that  the  size 
can  withstand  allowing  the  specified  factor  of 
safety,  which  total  includes  the  moment  due  to 

75 


76         HANDBOOK    ON    REINFORCED    CONCRETE. 

the  dead  load  of  the  concrete  itself  as  well  as  that 
due  to  the  live  load. 

To  facilitate  computations,  in  column  2  is  given 
the  weight  per  lineal  foot  of  the  beam,  from  which 
the  moment,  due  to  the  dead  load,  can  be  ascer- 
tained by  taking  a  trial  size. 

Column  4  gives  the  ratio  of  the  moment  of  in- 
ertia of  the  section  about  the  neutral  axis  which 
is  lettered  /,  to  the  distance  of  the  upper  layer  of 
fibers,  which  layer  in  all  cases  has  the  most  stress 
to  withstand  by  compression,  from  the  neutral 
axis,  lettered  y.  This  ratio,  of  course,  is  the 
same  as  that  of  the  safe  maximum  bending  mo- 
ment, expressed  in  inch-pounds,  to  the  safe  allow- 
able stress  per  square  inch  of  the  concrete  in 
compression.  It  is  given  more  as  a  check  than 
from  any  practical  use  it  bears  to  the  u^e  of  the 
table. 

Under  column  5  is  given  the  section  of  the 
steel  member  or  members,  which,  by  virtue  of 
being  embedded  in  the  concrete,  is  able  to  with- 
stand the  tensile  stress  in  the  worst  layer  resist- 
ing tension,  allowing  the  same  factor  of  safety  as 
was  allowed  in  the  concrete,  namely,  3.5  or  5.0. 
Of  course,  as  long  as  the  extreme  layer  remains 
strained  below  the  elastic  limit,  all  layers  ap- 
proaching the  neutral  axis,  which  must  necessarily 
be  less  strained,  are  obliged  to  remain  intact,  and 
there  can  come  undue  stress  on  these  layers  only 
after  the  extreme  layer  has  been  strained  beyond 
the  elastic  limit.  Accordingly,  in  designing  the 


DESIGNS    OF    CONCRETE    STRUCTURES.  77 

beam  for  tension,  it  is  necessary  only  to  put 
enough  steel  in  the  extreme  layer  to  withstand 
the  tension  in  that  layer,  allowing  the  proper 
factor  of  safety.  All  layers  approaching  the  neu- 
tral axis  will  have  their  corresponding  tensile 
stresses  properly  resisted  by  the  concrete,  as  long 
as  the  extreme  layer  remains  intact.  The  steel 
section  as  here  given  in  all  cases,  is  designed  to 
be  placed  in  the  beam  or  girder  with  its  lower- 
most part,  at  the  center  of  the  span,  just  1  inch 
above  the  underside  of  the  beam,  but  never  less, 
in  order  to  be  sufficiently  protected  by  the  con- 
crete in  case  of  fire.  At  the  center  of  the  span, 
the  location  should  never  be  more  than  1  inch 
above  the  bottom,  without  making  allowance  for 
the  lessening  of  the  moment  of  resistance. 

Under  column  10  is  given  what  is  termed  by 
the  heading,  "The  Proper  Size  of  Bars."  This, 
at  first- thought,  may  appear  uncalled  for,  as  long 
as  the  area  of  section  is  given,  but  after  reading 
what  is  outlined  under  the  "Tensile  Strength  of 
Concrete,"  in  another  section,  the  reason  may 
appear.  Briefly,  in  cases  where  it  is  required  to 
use  two  or  more  rods  to  equal  the  section,  a  num- 
ber might  be  selected  leaving  very  little  concrete 
between  the  different  steel  members  in  the  layer 
along  with  them.  This  total  resisting  area  of  the 
concrete  between  the  rods  might,  in  extreme 
cases,  be  so  reduced  that  it  would  be  incapable 
of  transferring  the  tensile  stress  from  member  to 
member,  because  of  an  excessive  stress  per  square 


78         HANDBOOK   ON   REINFORCED   CONCRETE. 

inch  upon  the  area.  In  such  a  case  it  might  be 
practically  impossible  to  work  in  the  concrete 
between  the  steel  members  without  leaving  voids, 
or  allowing  the  members  to  rub  together  with  only 
a  film,  if  any,  of  concrete  between.  With  this  in 
view,  the  items  under  this  column  were  so  selected 
as  to  leave  sufficient  area  of  concrete  between  the 
steel  so  that  this  latter  would  not  have  to  carry 
over  1,000  to  1,500  pounds  per  square  inch  in 
tension,  and  at  the  same  time  allow  space  to 
properly  work  in  the  concrete  between  the  rods. 
This  area  is  given  under  column  12,  and  the  cor- 
responding tensile  stress  per  square  inch  under 
column  13. 

Column  11  gives  the  distance  below  the  center 
of  gravity  of  the  section  to  the  neutral  axis.  This 
is  determined  after  the  steel  section  is  known,  and 
the  rods  selected,  by  substituting  an  area  of  con- 
crete, which,  when  placed  at  the  location  of  the 
steel,  would  give  the  same  tensile  resisting  power 
at  the  extreme  layer  as  does  the  section  of  steel. 
This  area  is  considered  attached  to  the  beam  so 
that  its  depth  is  equal  to  one  side  of  the  square 
rod  or  rods,  and  its  width  ten  times  the  total 
width  of  the  rod  or  rods  —  ten  times  because  the 
modulus  of  elasticity  of  the  steel  is  ten  times  that 
of  the  concrete.  By  so  doing,  we  obtain  an 
inverted  T  section,  and  it  remains,  in  order  to 
determine  the  neutral  axis,  only  to  determine  the 
center  of  gravity  of  this  section  by  the  method  of 
moments. 


DESIGNS   OF    CONCRETE    STRUCTURES.  79 

It  has  just  been  stated  that  the  steel  section 
was  so  designed  as  to  be  protected  by  1  inch  of 
concrete  at  the  center  of  the  span.  This  was 
fixed  at  1  inch  by  balancing  up  two  important 
factors,  each  directly  opposed  to  the  other.  For 
instance,  to  render  the  beam  or  girder  fire  resist- 
ing, it  is  well  to  have  the  steel  members  thoroughly 
protected  from  below  by  concrete,  wrhich  tends  to 
have  the  tension  members  approach  the  neutral 
axis.  On  the  other  hand,  in  order  to  obtain  the 
greatest  moment  of  resistance  in  tension,  the 
tendency  is  to  have  the  tension  members  approach 
the  underside  of  the  beam  or  girder.  Along  this 
same  reasoning,  in  order  to  prevent  hair  cracks, 
caused  by  excessive  tension  due  to  deflection, 
across  the  underside  of  the  beam  which,  although 
they  do  not  to  any  extent  effect  the  strength  of 
the  beam,  are  very  unsightly,  the  tendency  is  to 
have  the  tension  members  approach  the  under- 
side of  the  beam,  since  this  adds  to  the  stiffness  of 
the  beam,  and  thereby  lessens  the  tension  in  the 
concrete  below  the  steel.  By  equating  these  fac- 
tors, judgment  will  fix  the  location,  especially  at 
the  center  of  the  span,  about  1  inch  from  the 
underside  of  the  tension  members  to  the  under- 
side of  the  beam  or  girder. 

Finally,  to  give  an    outline  how  the  values  y. 

and  the  safe  allowable  resisting  moments,  both  of 
compression  and  of  tension,  were  deduced,  the 
following  routine  is  given: 


80          HANDBOOK    ON    REINFORCED    CONCRETE. 

Let  M  =  Maximum  bending  moment. 

b  =  Width  of  beam  or  a  width  of  floor 

corresponding  to  bending  moment 

above. 
d  =  Depth  of  beam  or  thickness  of  floor 

down  to  center  of  tension  members. 

M       1  bd? 

Then  — —  =  -     -  whence  assuming  b,  d  is  com- 
500        4  d 

puted. 

This  is  a  preliminary  step,  but  after  the  neutral 
axis  is  located,  and  using  the  value  of  d  just 
found,  the  fiber  stress  at  top  fiber  figures  about 
850  pounds  per  square  inch.  Calling  the  ultimate 
compressive  stress  3,000  pounds  per  square  inch, 
which  should  be  attained  in  a  1-2-4  or  a  1-1 J-3 
mixture,  the  stress  just  found  gives  a  factor  of 
safety  of  3£. 

The  next  step  is  to  find  the  area  of  steel  which, 
when  taking  all  the  stress  in  the  worst  position  of 
tension,  takes  a  stress  of  15,000  pounds  per  square 
inch.  This  is  figuring  a  factor  of  safety  of  3.5, 
with  an  ultimate  stress  of  52,000  or  53,000.  To 
do  this,  I  assume  the  neutral  axis  to  be  from  1.5 
to  2.0  inches  below  the  center  of  gravity,  and 
figure  the  area  of  the  steel  thus: 

M         ah2 


15,000        h 
Where  a  =  area  of  steel. 

h  =  distance  from  center  line  of  steel  to 
neutral  axis  assumed  above. 


DESIGNS  OF  CONCRETE  STRUCTURES.        81 

With  this  area  of  steel,  the  neutral  axis  can  be 
located  by  taking  moments,  after  transposing  the 
area  of  steel  into  an  area  of  concrete,  etc.,  as 
stated  before.  If  this  location  does  not  come 
sufficiently  near  1.5  or  2.0  inches  below  the  center 
of  gravity  of  the  section  to  fulfil  the  assumption 
previously  made,  use  this  value  to  determine  h  in 
in  the  last  formula 

M 

(Namely  =  ah),  and  solve  for  a  again. 

15,000 

This  new  value  of  a  will  probably  not  change  the 
location  of  neutral  axis,  found  previously,  enough 
to  effect  the  results.  Now  we  are  able  to  figure 
the  fiber  stress  of  the  concrete  in  compression  and 
so  check  the  850  pounds  per  square  inch  with  the 
sizes  we  had  determined,  or  else  fix  new  sizes  to 
give  no  more  than  850  pounds  per  square  inch 
for  the  concrete  in  compression. 


82         HANDBOOK   ON   REINFORCED    CONCRETE. 


1—  1         ^ 

b-    b- 


«        ^ 


oo   oo   <o  co         ^   r^   o 

Is-    Is*    00    O>  t"»    00    O 


S      §1. 


fe! 


£ 


I 


^ 


*^3535    ,. 


SSi      ^SiS§8 


a     *.<*. 


CD        OCOOO  OOOOO 

D        1C    OS    b-    ^  1C    00    1C    1C    O 


o  o  o 

CO  CO  CO 

rh  CO  iC 

i-T  csf  co" 


«5    O    O    O  O    O    O 

-H    O'  »C    1C  1C    >C    10 

S    M    CO    ^  rH    N    ^ 


«;   OOOO     OOOOO     OOO 

£    coc32!2      tSioS^M      ^w^ 

^  r-T  <N"  co"  rn"  CN  w  »o        <N"  co"  10 


l>    U5    1C 


J        l>>C»Cb.  OSOOOiCCO 

£  i-lC<ICO  i-lCOT}<cO 


O 

CO 


So 
COCO  •*b-^<NO  b-rHTjH 

ooo^     d?ic§Sbi     S^K 


"^        ICO1CO  OO^fOcOCNI  WOOO 

r*       T-HCNCMCO  rHCSlCOCO^  CO1^^ 


GO     <N  »C  CO     CO  l>  O 

00  1C  i-I  b.'  CO     CO  i-I  O 


O  CN1  O  CM  ^        O  Cl 

XXXX    XXXXX    XXX 
csi  ^ 


DESIGNS   OF   CONCRETE   STRUCTURES. 


^OOOOO  i"* 

CM      l^«      -^1      CO      rH  T-H 


t>    00    O>    O 


CO    TiJ  <NT(<Tt<OO<O  <N  1^  O  >-i  CN  <N  CN  COCN<NOOOSOiOO 

»H    <N  p    I>    00    O    O    O  t>  00  p  I-H  CN  <N  p  OOOSppOCiCSO 

COCO  CN    CN    (N    CO    CO    CO  CO  CO  "tf  •<*  Tt<  "*  ^  COCOCO^-^COCOTt! 

SCO  CO  |Ci    O    <N    1C    CO  CO  »O  GO  O  00  >-i  CO  OOU300t-OCNTt<O 

O  O  I-H    CN    Tt<    10    t^  O  CN  CN  TJ<  TJ<  10  CO  CO»oiocb£iOCOI> 


J<o  coto         into         i_|to  into  Jo 

rH    I-H  1.NCNCNCNCNCN  CN    CN    CN     CN    CN    CN     CN  COCOCOCOCOCOCO 


OO  OOOOOO  OOOOOOO 

CO     CO  lOi-HiOOO^O  rH     T-H     CN     CO     00     O     *O 


iQiO  OOiOO'O'O'O 


C35  col        10"  rT  co"  oo  co   i>         co"  oo  t>T  I-H"  oT  CN"  oo         co"  rC  co  o"  -H"  10" 


o  o  o  o  o 


oo        ooooooo 

»-i     rH  COCNTtl»OOOi-HCO 


00    rn    »O    00  t-    O 


o"  TjT  oo*  CN"  t>T  co"        of  co  r-T  co"  CN   od  »c 

iHi-li-(C<IC<JCO.       T-lr-(C<ICNCOCOTtl 


T|<    CN  O    *O    »O    O    O 

00    1-1  »O    t^    O    •*    00 


b»  «D  *    p  o    go        oo  t>    <N  10 

<NCOi-ir^COO5  -^OSiOi-i 

i-li-HCNCNCOCO  ,-JrHtNCO 


•       •  Or^T^COOOMCO  OO5COCNOCOCO 


CO-*  OOOOOO  cN-*cOOOOCNTt<  COCN    CO    O    T»<    oo    CN    CO 

U5«0  »OCOt^OOO>0  t^OOOJOCNCO^  OS^HCN^iOCOCOOS 


CN    p  p    CN    »O    CO 

00    CO  CM    CN    CO    CO 

lO     CO  W     CO    t^     00 


XX   XXXXXX    XXXXXXX    XXXXXXXX 


HANDBOOK   ON    REINFORCED    CONCRETE. 

'35  $  §^'^  & 


JiW! 


. 
9  M  £  c3     • 

• 


S3 

II: 


;ooo>oioooioo        oooo 

;Tfit^iO<NOCOCO>— i     <N  CO    W    1-1    TH 


§  8  8  § 


H5 


CO      CO      Tt<      T(H 


co  OOOOOOOOO  OOOO 

^O  (NCOCOC^QOCOOOC^  OOOOOCO 

+J  CO     CD    r-T    iO     O"    CD     Ci    Oi"    CO  CO     CO     OJ     ^ 

p^  r-ti-HC^CMCOCO^^^O  i-tOlC^CO 


I    8  S  S  §  8 


ooooooo 

^00>000(MOt- 


000 
»  *  35 

00    »C    l> 


CO  •*     »0 


SCO     CO     1C     CO 
O5    C5    O    <N 
^H  CO     TP     CO    t^ 


M    O    00    CO 

CO    00    O5    —  i 


t,    - 

i 

*"* 


00    t~-    CO    U5 

CO    00    O    (N 


•g      XXXXXXXXX         XXXX 

^        000000000000000000  OiOi«5O5 


DESIGNS    OF   CONCRETE    STRUCTURES. 


85 


I-HOOOOO        »co>oioooooooio        o  10  o  o  o  o  u: 
osoor-^oios         oiosoocoo'Ci-HOicoosio         -^   T-I   as   o   os   co   t^ 

CO    O    i-<     Ol     T)<     Tf  OOr-fOlOOrHOIOlOlCO  O)     CO    CO    O4     O)     O    C 


§h.  ,-1  i-<  O  O  Gi-ii-ii-iO500>CiCOOCO  O  Ol     Ol    O    O    1C    CO 

»C  l>  I>  01  01  Or-iWOJp'-iOIOlCOCOCO  p  •-!    1-1    »O    >O    t^    00 

1C  CO  CO  CO  CO  CO  COCOCOCOOOOOOOOOOOOOOO  CO  CO  CO  t~  t^  OS  OS 

O    O  O  »0  TP  h.  t^OSOCO©00»OOOOOTi<  <N<NOO(NU5 

OS    t^  OS  OS  O  O  COCOOOOOt-t-OOOOOi-ii-H  00  OS     OS     OS     rH     t-     00 


JJU 

3  3 


,HS 


>O    CO    0} 
OJ>M 


rt<    f-    CO  OCOO<MOC«3 


S  §  5  S 


oooo  ooooooooooo 

1-1     »O     O     O  i-iOlCOOOJiCOCOt^OOCO 

Oli— ICO^C  COCOt^-iCCOOlOCOCOOli— t 

ic  co"  t-T  o"  co  of  06"  <c"  co"  i-*"  o   oT  os"  o^  i-T 


1C    ^O    O    ^     ^*     C^     IO 

io   <M"  o  oo  t-T  tC  iC 

co   •*   10   »o   o  i>   oo 


iC»CiCO  OOOOOOOOOOO  OOO^COOO 


oo"  to"  oo  o* 

»O     CO    1>     OS 


OOOO 
00    IM    (M    O 

00    O    of    10" 
1>    OS    O    rH 


tCt-CO»C  CO«CO^O)O1 


iciccot-ocor^i-Hoo         o  o  i- 1  co  to  o 

iOcO^-OOO'-iOIMH»C  lOcOt'-OOOS'-i 


CO     Ol"    tC    o"  I-H"    T^    ~rf    O"    -^    O"    o"    10"    of    of    1C  o"    Os"    00     Ol"    tC    1C 

•^OOOIOO  »CiCCOOOi-H»COCOCOOO  i-HOJiCOiCOl 

OSOOICO  TjilCCOt^OSOOlCOiCt^OS  CO     Is*     00     O     i— 'CO 


COOOOOOt^iO  OOOliCiC 


»O    O  O 

CO      i~<  TJH 


CO      "^      i—(      i—  * 

oo  o  oi  -* 


3OOOOOOOOO  OlTfHcOOOOOlTM 

MTfcOOOOOl^COOOO  TflCOOOOCOiCt- 

NOlOlOlCOCOCOCOCOrf<  OIOIOICOCOCOCO 


.  <. 

OOO»-iCO  OOl«Ct~-.O3rHCO»CI>.OSi-H  lCt>-OSOlTtlCD 

04COCOCO  040)04O1OlCOCOCOCOCOrt<  OIO1O1COCOCO 


COOOOOlrlHcO  OO)rt<cOOOOOjTt*tOOOO  Ol^tDOOOOlTfl 

OlOJCOCOCOCO  040401010JCOCOCOCOCOTJ<  OI010JOICOCOCO 

X  X  X  X  X  X  XXXXXXXxXXX  XXXXXXX 

OSOSCSOSOSOS  OOOOOOOOOOO  rHrHrHrHr-I^H^H 


86          HANDBOOK   ON   REINFORCED    CONCRETE. 


.    r<    *O      *O      *O      *O      *O  lO^OOOO^OOOO 


oo«o^t-M<coo«'-i'—  i 

r-it-OOOOOSOSCOOOOO 


d    .    <n 

' 


CO    CO    CO    CO    CO 


.2        **    00    01    CO    OS  lOO'OOSCOcOr-iT^CTi 

61       l>    I>    00    00    00  iOcOCOCOl>t^OOGOOO 


Us 


oooo   oooooooo 

Tf     CO     O    1~-  COCOOOiOOt^OSCO 

rH      O      OS      I-l  TjHCDOOCDOCOCOlO 


8  8  S 


GO  00 
r-i  t^ 
CO  1> 


l 


ooooo   ooooooooo 

CO1>OSOO)COIOCOOO 


fl      cq  oo  o  co  «s         t»  o»  o_  <N_  TJ^  «o_  oo_  o^  N 
i-T  t-T  of  of  of  r-T  i-T  r-T  I-H"  i-T  of  of 


OIO 


OICO 
i-HCO 


CNCDO 
COiOOO 


lO  00 

2'  %  S  ss 


S  COOOOOJ-*  r^cOOOOOlTjfcOOOO 

J  COCO^T^rtl  OIOJOICOCOCOCOCO^ 

2  XXXXX  XXXXXXXXX 

(-(  rHi-l^-I^HrH  NO1O1NNO10101O4 


DESIGNS   OF   CONCRETE    STRUCTURES. 


87 


O    O    O    »0  OOCOCOCOOO**CO<NOOOCO 

OS     OS     OS     OS  COCO^-tf-tflOlOlOiOOOCSOSpp 

,_;,_;,_;,_;        odoooOQOQOOOQOcoeocQ'*'*        as  as  o  os  <N  <N 


O      '    «    10    O    O    O    O 

rH  00      O      rH      00      OS      O 

N  rH      CN      &\      rH      rH      C<1 


OS     O5    O     O 


"*. 

06  06  06  os 


o  o  o 

IQ      T-H      |> 

00    10    i-^ 


§    00    «3    O    <N     00  <N 


o  o  o 

<N    CO    •<* 

-^  I-H_  10 
" 


00    OS     I-H     <N 


CD  00  O 

(N  t^  CO 

t>-  GO  O 

i-T  r-T  of 


O      rH      CO 
rH      CO      1O 

I>    CO    OS 


§0  00 

iO  *O    *O 

|>-  C^     t^- 

CD    00  00    O 


t>    CO    O    CD 

rH      CO      »O      CO 


-t  1C  CO 

1C  CO*  .-H~ 

O  <M  Tt* 

CN  <N  (N 


§2g£ 

TP      t^      O      rH 


§  s 

t^    OS 

96  of 


O    O    O    O 
i— t    »O    "^    t^ 


>O  IO 

•<*  t» 

rH  CO_ 

<N~  (N* 


CO      CO      00      rH 

CO     CO     CO     "# 


O    01     10 
iO    1C    IO 


GO     "^     O     CO     C<l 

CO     CD    OS     rH     Tf 


(N  O  00  CO 
OS  (N  rt*  t- 
CO  Tti  "*  •* 


i/5O«O 
(NiOt>. 


>O 

t^ 

O    CO    CO 

^      «*      t 


rfl-^Tf<Tti  C^IMCOCOCOCOCO^TtiTtiTti^iCiC  C^COCOCOCOCO 

XXXX    XXXXXXXXXXXXXX    XXXXXX 

N<N<N<N  COCOCOCOCOCOCOCOCOCOCOCOCOCO  Tj<Ti<T}iTt<Tj<Tf 


88         HANDBOOK   ON    REINFORCED    CONCRETE. 

rfdgSSSSSSgS      °,£ 


,J  cr 


$ 


1C    »C     0    00    00 
CO     CO    CO    CO    CO 


O    O    O    O    >O 
t>    t^    CO    00    00 


O         <M<M(Mi-HC^(M<N<N<N  rH     ,-<     r-l     r-H     r-( 


HOC  rtloo  «(5 

<N    <N    <N    <N    <N    <N 


4,  4,  4n 


OO'-i<-iCXl<NCOCO-Nt<  OOOOO3OO 


o5        OOOOOOO 
n        "^f    ^    Tf    10    CO    >O    T— i 

±;      cor-io>tN.'-H<Nc^ 


o  o  o  o  o 

00  CO  ^  IN.  10 

ci  Tf  OJ  •**  OO" 

OS  O  T-I  CO  rji 


11 


OO 
O    ^O 


^        CO    O_    --H 


O>-ICO>OOOOCO»O  I-H     W     Tt<     CO 


3          «4-       • 

i 


OC^IfO 


00  t^,  CO  CO  »O 

co"  ^  S  of  2" 


»O      IN.      O      O 

OO    Tfi     O    >O 
t>    O    CO     IO 


GO  >O  00 

^H  CD  00 

O3  r-l  •* 

r^  (N  C4 


jf 


10     O  O  O  O  O 

00     U5  00  >-i  ^  b- 

1>        TjH   Tfl   IO   »O   IO 


. 


b-     00  O  O  IN 

,-!     CD  O  CO  CD 

00    ^  o  o  m 


xxxxxxxxx   xxxxx 


DESIGNS  OF  CONCRETE  STRUCTURES.     89 

IO»O»OIO»O»OO  OOOiOOOiOOOO  O>OiO 

I-H     CO     »O     O     Tfi     h-     O  GOC500COCOOOINOOCOCO  O5lN»O 


OOiOO»O»OiO»OiO»O 

»-ICO 


<N<N<N(NiOiQ»OiOiO 


O  O    O    *-i 


r-i     <N     IN     <N     <N     i-H     IN     <N     <N     <N     <N  THiHNWi-li-li-lWNi-l  rH     rl     <N 


TjH      Tt<      Tf      T)<      T« 


^COCOCOCOCOCO  lOiO^OlOTf 


2  ||  S 

(N  CO    oT  TJH" 

t>.  OS    *— i  ^ 

<N  IN    CO  CO 


ooo 

>OCOCO 


oooo 


OOO 

Sao    10 
00    M 

S  2'  d 

04     CO     CO 


o  o  ^o  o  *o  o  »o 

i— i     O    C^     iO    t^»    O    t^- 


§  § 

O    1C 


co"  co" 


i-l     <N     <N     (N     (N     CO     CO 


T}<      •Tfl  1-H      l-H      I-H      I-l 


1C 
N 

10  a> 


O  O 

N-  IO 

CO  <N 

CO  ^H" 


OOO 

S  8  8 
S3  S  g 

CO     CO     05 

co"  co"  co" 


§ 


888 

iO    O    iO 


iO    iO    >O    CO  I-H    IN 


CO     CO     CO     CO 


10"  10  10 


S  8  ° 

O    TJH    00 


SSi?: 


CO-tfOOOiOOOOCOiN 
COcOO3COCDO^Ht^-'-iCO 
(N(NINCOCOTt<-*T}HiOiO 


O    <N 


o  o 

<N       IO 


O    O    O    O 

00      rH       Tf       (^ 

l>    00    00    00 


(N    •* 

CO     CO 
00    00 


1^    00    O 

CO     i-H     >O 
CO     t^     l> 


I-H    CO     t^    iO    t^ 


O5O5  lOiOCOCOCOt^-t^t^OOOO 


xxxxxxxxxxx 


(N-*COOOO(NTfcOOOO  (N-^cO 

COCOCOCO-^TfiTtlTti'»t|iO  IO»OIO 

xxxxxxxxxx  xxx 

COCOCOCOCOCOCOCOCDCO  COCOCO 


90         HANDBOOK    ON    REINFORCED    CONCRETE. 


«        S  g 85  § 


r=c 

J|i 


8282 


li 


8^88  28882 

^i    i-H    (N    IN    <N    r-I    (N    <N    (N 


U5iOiO»OiC»O 


i 


.££338      §3S£S18388S 


.    - 


8  8 


(N    O    00  1C    rH 


4OOO 

IN"  t^  -o' 


•          Oi     O     Tt*     t^- 

c      co   i>   o   co 


r-lTH(N(N(N<N<NCOCOCO 


»O(NOIN  <NCO»OOOOCO 


•^  1C  *O  O  *O  >O 

CO  <N  O  CO  »-i 

C  d  t^-  C<l  CO  CO 

CO*  CO"  t^  t>T  <N 


^-^O^OOOO^O 
N»OC5'-ilOC5CO 


C3         OOOC^Tt*  OOCNCOO-^COINCOO 


.SP«  8"S 

<1J  Q.C  C 


co   r-~ 

CO     CO 
O    O 


15  1   s 

sJo-H 

CO          bC 


2         »OCOCOCO  COCOCOTtiTtiTtlTjiT}<iCiO 

g      XXXX        XXXXXXXXXX 


DESIGNS  OF  CONCRETE  STRUCTURES.     91 


O    O    iO    »O    O    iO 

—i   *o   oo   <N    o   os 


OOO>OOO»OOO 

-H.-iiooocort.-HcO'^ 


OO<N<N»OIOOOO         lOTFooco 

OCOCOt>-l>.CSpp  b-p'-i'-it>. 

2  88  Si  S3  Si  SS  S      S2222 


•V  "><  H-i  HM  Hci  *M 


<N     <N     <M     <N 


^t_^^r- 


t^t^OOOOOS 


O  O     <N 
<M  W      rH 


OS  OS  O  *— '  i-4 
<-t  .-H  <N  IN  (N 


O  O  O  O 
>O  CO  00  »O 
<N  CO  O  <N 


O  CO  CO  T-I  00  »O 


-. 

§T)H   r^   o   10  --H 
M    CO    O    CO    b- 


t~-  t>-  OS  00 

OS  ^  -H  rf 
CO  CO  OS  O 


COCO     r-l(N(N(N<NC«5COCOCO-^-*rJilO»O'-OCO 


0    O^    00    "3    O    00    00 

'" 


<NlOCSCOCOI>COOS»OTfri 


O>OOOOOO  »O'O»OC<IO'OOO>OO'O»O»OOOO»O 

*^    00    ^O    !O    CO    »— '    ^O  COCOC^OOts-|OCOOC^OtN"tN-COO^CCOO 


o>ooooo        1010010 

OOOOOSOiOi"*  COCO^Tt^ 


S  8  S 


cS  o"  i-J"  i-T 


00  (N  CO  O 
(N  CO  OS  CO 
OS  O5  OS  O 


3  8  $  Ss-  3 

CO  b~  t^  t^-  00 


<NOO'*OCOMOO'* 
h-O'fOO'-iiOOOM 
OSOOOi-l»Hi-iC<l 


iOiOiO»O>O»O«5'O 


lOO^OOiOO^OO  »OCN 


^COOOO<N-*cOOO  cOOOONTjicOOOdlN^COOOOIN^COOO 

IO>O»OCOCOCOCOCO  COCCTf<Tfirtir}iTtf»O»OlO»O»OCOCOCOCOCO 

xxxxxxxx  xxxxxxxxxxxxxxxxx 

b.t^t^t^t>t^f^t^  OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOQO 


92         HANDBOOK    ON    REINFORCED    CONCRETE. 


00*000000*0 

iOOiCOO3'OCOt>.rtiO 


COOO>O»OC5OO 
O5O<NCOCOCOiO«O 


82 


OOOOOiOCOO>OOOO 
OOOOOiOOOOt-H 

rH    (N    (M    CM    I-H    T-I    (N    (M    01    CN 


•         o    >O  h-    O 

.«         10    p  CO    I-H 

r/T        <N     <N  rH     T-t 


OOCOON-cMOCOCN 


OCOCNiO 
Ol^COO 


|-o! 

S  2  o 


^        OiO  (NCNOOOt^'—H'^t<OOOlOlO 


f— '     M  COCOOOt>-r— iC^TjHioO^O 


h 

il 


O     O  CO 

CN     O  CO 


Slili 


$    O 

o"  i-T 


O*   t^-"   tO^Ot^-^O^OO^OOC 
CO-— iOOO5C33fOOiTtiCOCOl^ 


CO     O 
O'-H 


<NOO<NO 


OO 
i-(»O 


•!   XX    XXXXXXXXXXX 


DESIGNS    OF    CONCRETE    STRUCTURES. 


93 


OOOOOO»OiOO  »OiCO»O»O 

t-t-i-i^cooiNico         Nfc»o5t»e9 

COi-ii-ii-ii-iO4CM<N<N  i-i^fNCMCO 


COCOiC<NcM 


OOOOOOOOOOO 

i-i  p  p  p  p  p  op  <N 

<N    T-i    <N    <N    <N    <N    <N    <N    <N 


l^CNCOOOOCOOiOCOOCOCOOiOO 

oo  9  0»  ,o  »4  ••*  *-<  Qi  o  *-<  1-1  *4  ei  0  o 

r-i    ,-1    r-<    <N    <N    CM    CM    r-i    CN    <N    CM    <N    <N    i-f    <N 


^cocococococococo         J> 


.555^.^!* 

£  3  s  2  3 


cOO^CMcO<Ni-HCOOOCMCOi-iiCiO 
TtH<MOSt^C5Ol>CMpCOCOpt>T-iO5 


poqicppt^Oi_wcq 

i— <iCOOO*Oi— 't^^cO 
OCMiCCSCMCOCSCOt>. 
TtiTfiTffTjiiCiCiCCOCO 


CM  ^f  CO  00 
<M  (N  CM  CM 


o"  as"  co  o"  os"  ic  <M"  o"  <N"  o*  o"  <-*"  »c  <N"  o" 

TPCOOO'-H-^lt^i-ii-iOOOO-*t>-i-iW 
OSCMCOt^-OCOOOi^^COOCOI^i— iCOi-^ 


&  So 


00      CM      t^      I-H       CO      r-l 

"' 


ooooooooo 
cococor^oi>cococo 

OOCOOOCO'CCOOOCO_CO_ 

ic"  co"  o"  TH   <N"  co"  o   oo"  co" 
cOi-Hcor-HcO'-ir^iMoo 

COI>I>OOOOOSOSOO 


CD  --I  CO  O  00  OS  CO 

^  n  if  «  o"  IN  oo" 

00  O  ^t1  00  C^l  1^*  O 


000 

t^    1C    t^ 

1-1     <N     CO 


8  § 

I>  I> 


o  o 

iC  O 


COGOCOI>CMOOCOOOTfiOCOcMOO 


00    OS    OS    O    O    I-H 


8OOOOOOOO  OiCOOiCiOOOOOOOOO 

OSOOOCO'^'^t^-t^-  C^OSC^I^-CMi-HOS-^iCCOOOcMt^-^ 


O    00    CO 


S  8 


oooooooo 

'*OOCNCOO'<*I00(N 
OOi-irHCMOJCMCO 


V       W  ^J        "V        1-        t-       ^^' 

r^   I-H         co   t^-   i-i    ws   o 

•*    »C  00    00    OS    OS    O 


O<N-^COOOO<N<*CO  OCN-^OOOOCMT^COOOOCM^COOOO 

C0cocococ0t^t^t^-t>-  TfTtTtiTti'*iC»C>CiC»CcOCOCOcOcot>- 

xxxxxxxxx  xxxxxxxxxxxxxxxx 

i-lt-lr-Hi-li-lr-li-li-li-!  CMiM(NCMCMC^<MC^CM<MCNCSC^C^CNCM 


94        HANDBOOK   ON   REINFORCED   CONCRETE. 


- 


oj 


•        Tfi    O    O    O    iO 
.S        00    0    0    1-1    <N 


CO    CO    CO    CO 


o 

<N     (N     <N     (N     IN 


(N  M  CO  CO  CO 
1  1  1  1  1 
CO  CO  CO  CO  CO 


« 


_:      o  <N  o  co  t> 

.S        50  <N  00  CO  CO 

rj«       1C  ?D  CD  ^  00 

(N  <N  (N  (N  (N 


-It; 


•  Tf  CO  O5  CO  O5 
ff  I-H  iO  O5  rf  00 
^  t-  t^  t^  00  00 


r^   oo  os   <N   co 

«O_    O_    *O_    rH_    <O 
00    O5    O5    O    O 


o  o  o  o  o 

CO  »O  l>  O  O 

00  IN  CO  O  O 

p  i^  *-<  >O  O 

<N  00  •*  O  l> 

0  0  T-H  (N  <N 


o  >o  o  o  o 

fl        iO  t-  O  CO  •<* 

hH        (N  OJ.  t>;  -*_  <N 

<N*  M"  CO  O 


O    iO     O    CO 
"      ~ 


«««  i  a 

jiHJ 


0*0*0 
TP  00  (N 
10  iO  CO 


-a 


<N    •*    CO    00    O 
|>    t^    O    l>    00 

X  X  X  X  X 


DESIGNS  OF  CONCRETE  STRUCTURES.          95 

NOTE. 

With  single  spans,  fixed  at  the  ends,  place'  a 
reinforcement  in  the  upper  side  of  the  beam  or 
girder  forming  a  cantilever  from  the  fixed  ends 
extending  toward  the  center.  The  total  area  of 
this  reinforcement  should  be  66.7  per  cent  of  that 
placed  in  the  lower  side  as  called  for  in  Table  I. 
The  distribution  of  this  reinforcement  should  be 
as  stated  in  the  description  of  Tables  la  and  16 
for  the  reinforcement  in  the  upper  side  of  contin- 
uous girders. 

When  figuring  girders  of  more  than  one  span, 
having  fixed  ends,  make  the  following  changes  in 
the  amount  of  reinforcement  just  given. 
With  2  spans  decrease  'the  amount  by  44.6 

per  cent. 
With  3  spans  decrease  the  amount  by  36.0 

per  cent. 
With  4  spans  decrease  the  amount   by  38.3 

per  cent. 
With  5  spans  decrease  the  amount   by  38.0 

per  cent. 

With  6,    7,    8,   and    9    spans,    decrease   the 
amount  by  38.0  per  cent. 

DESCRIPTION  OF  TABLES  la  AND  Ib. 
The  following  tables  are  inserted  to  allow  for 
the  effect  of  continuity  of  beams  or  girders  over 
one  or  more  supports,  and  give  the  proper  steel 
sections  to  withstand  the  bending  moments  given 
when  produced  by  a  uniformly  distributed  loading 


96         HANDBOOK   ON   REINFORCED   CONCRETE. 

over  equal  spans.  When  these  conditions  do  not 
exist,  it  remains  for  the  designer  to  ascertain  the 
bending  moments  in  the  different  spans,  ignoring 
the  effect  of  continuity,  as  this  is  cared  for  in  the 
results,  and  to  fix  upon  the  size  of  concrete  girder 
that  will  care  for  the  largest  moment  thus  found 
by  referring  to  the  table.  Opposite  the  size  just 
determined  will  be  found  the  reinforcement  to 
adopt  for  different  parts  of  the  girder.  Table  la 
is  worked  out  for  two  spans.  Likewise  Table  Ib 
is  for  three  spans  only,  but  is  applicable  to  any 
number  with  a  maximum  error  of  1  per  cent  for 
moments  over  supports,  and  that  on  the  safe  side. 
For  moments  within  the  spans,  the  following 
changes  should  be  allowed  in  the  intermediate 
spans,  the  outside  spans  remaining  as  in  the  table. 
With  4  spans  increase  the  reinforcement  in  the 

intermediate  spans  by  46  per  cent. 
With  5  spans  increase  the  reinforcement  in  the 

intermediate  spans  by  85  per  cent. 
With  6  spans  increase  the  reinforcement  in  the 

intermediate  spans  by  74  per  cent. 
With  7  spans  increase  the  reinforcement  in  the 

intermediate  spans  by  76  per  cent. 
With  8  spans  increase  the  reinforcement  in  the 

intermediate  spans  by  74  per  cent. 
With  9  spans  increase  the  reinforcement  in  the 

intermediate  spans  by  74  per  cent. 
In  distributing  the  reinforcement    given  in  the 
tables  for  continuous  girders,  the  following  plan 
may  be  suggested: 


DESIGNS    OF    CONCRETE    STRUCTURES.  97 

All  rods  in  the  underside  of  the  girder  should 
extend  from  support  to  support;  .3  square  inch 
of  steel  per  square  foot  section  of  girder  in  the 
upper  side  of  the  girder  should  extend  from  sup- 
port to  support  and  lap  sufficiently  to  develop  the 
elastic  limit  of  the  section  by  exposing  a  sufficient 
surface  to  adhesion  between  the  steel  and  the 
concrete;  one- third  of  the  remaining  section  in  the 
upper  side  of  the  girder,  should  be  one-half  the 
length  of  the  span  and  center  over  the  support. 
Another  third  of  the  remaining  section  in  the 
upper  side  of  the  girder,  should  be  one-third  the 
length  of  the  span  and  center  over  the  support. 
The  last  third  of  the  remaining  section  in  the  upper 
side  of  the  girder,  should  be  one-fourth  the  length 
of  the  span  and  center  over  the  support. 

NOTE.  —  The  purpose  of  the  continuity  of  rods 
in  the  upper  surface  is  to  care  for  tension  caused 
by  an  increase  of  temperature. 

The  object  sought  in  preparing  these  tables  was 
to  free  the  designer  of  the  tedious  routine  in 
determining  the  bending  moments  in  the  different 
parts  of  continuous  girders.  All  spans  of  the  con- 
tinuous girder  should  be  treated  as  single  spans 
supported  at  the  ends  to  determine  the  maximum 
moment  from  which  the  girder  size  should  be  as- 
certained by  reference  to  the  table.  It  may  be 
unnecessary  to  state  that  it  is  expected  that  the 
same  size  of  girder  section  will  be  used  through- 
out the  length  of  the  continuous  girder  as  deter- 
mined by  the  maximum  bending  moment  in  the 
different  spans  of  the  girder. 


98         HANDBOOK   ON    REINFORCED   CONCRETE. 
TABLE  la. 


1 

2 

3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

Size  of  • 

1            ,, 

Safe  bending 
moment. 

over  central  sup- 
port.    (In  upper 
side  of  girder.) 

throughout  spans. 
(In  lower  side 
of  girder.) 

beam. 

Factor  of 
safety  =  3.5. 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In: 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

2.5X6 

7,800 

650 

.47 

1-yi" 

.27 

l-is" 

2.5X8 

15,350 

1,280 

.52 

1-f" 

.29 

1-iV 

2.5X10 

25,250 

2,100 

.65 

l-yf" 

.37 

1-f* 

2.5X12 

37,800 

3,150 

.66 

1-tt* 

.43. 

1-H" 

3X6 

9,380 

780 

.48 

1-f" 

.27 

i-A" 

3X8 

18,450 

1,540 

.59 

i-H* 

.33 

1-f" 

3X10 

30,000 

2,500 

.66 

l-ll" 

.37 

1-f" 

3X12 

45,500 

3,790 

.78 

H" 

.44 

l~tt* 

3X14 

63,500 

5,290 

.88 

1-lt" 

.50 

i-r 

4X8 

24,500 

2,040 

.75 

H" 

.42 

i-H- 

4X10 

40,500 

3,380 

.86 

1-if" 

.49 

i-fr/ 

4X12 

60,500 

5,040 

.99 

1-1" 

.56 

i-f 

4X14 

84,500 

7,040 

1.14 

1-1  T&" 

.64 

i-^f" 

4X16 

112,500 

9,380 

1.26 

1-lf 

.71 

i-l" 

5X10 

50,650 

4,220 

1.15 

2-|" 

.65 

i_if* 

5X12 

75,600 

6,300 

1.32 

2-  it" 

.74 

i-f 

5X14 

105,500. 

8,790 

1.46 

2-f 

.82 

!—  H* 

5X16 

140,500 

11,710 

1.68 

2-lf" 

.95 

1-1" 

5X18 

180,000 

15,000 

1.86 

2-1" 

1.05 

1-1  A" 

5X20 

225,500 

18,790 

2.06 

2-lf5" 

1.17 

i-if 

6X12 

91,000 

7,580 

1.53 

2-f 

.86 

i-jr 

6X14 

127,000 

10,580 

1.78 

2-lf" 

1.00 

i-i" 

6X16 

168,500 

14,040 

1.97 

2-1" 

1.12 

1-1  A* 

6X18 

217,000 

18,080 

2.19 

2-1  A' 

1.24 

i-if 

6X20 

270,500 

22,540 

2.40 

2-lf 

1.36 

2-1" 

6X22 

332,500 

27,710 

2.62 

2-lf 

1.48 

2-f 

6X24 

398,500 

33,210 

2.84 

2-lf 

1.61 

2-lf 

DESIGNS   OF    CONCRETE   STRUCTURES.  99 

TABLE  la.  —  Continued. 


1 

2                    3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

over  central  sup- 

throughout spans. 

Size  of 
fc)63,rn. 

Safe  bending 
moment. 

port.     (In  upper 
side  of  girder.) 

(In  lower  side 
of  girder.) 

Factor  of 
safety  =  3.5. 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

7X14 

148,000 

12,330 

2.14 

3-1" 

.21 

l-ll" 

7X16 

197,000 

16,420 

2.41 

3-M" 

.36 

2-1" 

7X18 

252,500 

21,040 

2.62 

3-  if" 

.48 

2-1" 

7X20 

315,000 

26,250 

2.87 

3-1" 

.62 

2-lf" 

7X22 

387,500 

32,280 

3.11 

3-1  A* 

.76 

2-lf" 

7X24 

464,500 

38,710 

3.27 

3-1  A" 

.85 

2-1" 

7X26 

547,500 

45,630 

3.53 

3-1  A" 

2.00 

2-1" 

7X28 

639,500 

53,290 

3.77 

3-ir 

2.14 

2-1  iV 

8X16 

225,000 

18,750 

2.63 

3-  if" 

1.49 

2-|" 

8X18 

288,500 

24,040 

2.90 

3-1" 

1.64 

2-M" 

8X20 

360,500 

30,040 

3.24 

3-1  A" 

1.85 

2-1" 

8X22 

442,500 

36,880 

3.55 

3-lJ* 

2.01 

2-1" 

8X24 

531,000 

44,250 

3.82 

3-l|" 

2.16 

2-1  A" 

8X26 

625,000 

52,080 

4.09 

3-1  A" 

2.32 

2-l|" 

8X28 

725,000 

60,420 

4.32 

3-1  A* 

2.44 

2-1*" 

8X30 

840,000 

70,000 

4.65 

3-11" 

2.63 

2-1  A" 

8X32 

962,000 

80,170 

4.97 

3-1  A" 

2.81 

2-1  A" 

9X18 

324,000 

27,000 

3.38 

4-  W 

1.91 

2-1" 

9X20 

406,000 

33,830 

3.73 

4-1" 

2.11 

2-1  A" 

9X22 

498,500 

41,540 

4.03 

4-1" 

2.28 

2-l|" 

9X24 

597,000 

49,750 

4.37 

4-1  A" 

2.47 

2-1*' 

9X26 

702,500 

58,540 

4.65 

4-1  A" 

2.63 

3-M" 

9X28 

800,000 

66,660 

4.73 

3-li" 

2.68 

3-1" 

9X30 

946,500 

78,870 

5.22 

3-lf" 

2.94 

3-1" 

9X32 

1,082,500 

90,210 

5.54 

3-lf" 

3.13 

3-1  A" 

9X34 

1,227,500 

102,290 

5.87 

3-1  A" 

3.31 

3-1  A" 

9X36 

1,380,000 

115,000 

6.16 

3-1  A" 

3.48 

S-lf 

10X20 

451,000 

37,580 

4.10 

4-r 

2.32 

3-F 

10X22 

554,000 

46,170 

4.43 

4-1  A" 

2.51 

3-lf" 

100      HANDBOOK   ON   REINFORCED    CONCRETE. 
TABLE  la.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

Safe  bending 

over  central  sup- 
port.    (In  upper 

throughout  spans. 
(In  lower  side 

Size  of 

moment, 

side  of  girder.) 

of  girder.) 

earn. 

safety  =3.5 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft,  Ibs. 

Sq.  in. 

Sq.  in. 

10X24 

664,000 

55,330 

4.90 

4-li* 

2.77 

3-1" 

10X26 

780,000 

65,000 

5.12 

4-li" 

2.89 

3-1" 

10X28 

914,000 

76,170 

5.40 

3-lf" 

3.05 

3-1  A* 

10X30 

1,050,000 

87,500 

5.73 

3-1  A* 

3.24 

3-1  A* 

10X32 

1,200,000 

100,000 

6.09 

3-li" 

3.44 

3-li" 

10X34 

1,365,000 

113,750 

6.71 

3-  \-\" 

3.79 

3-11" 

10X36 

1,532,000 

127,670 

6.80 

3-1  A" 

3.85 

3-1  A* 

10X38 

1,702,000 

141,830 

7.14 

3-1  A* 

4.03 

3-1  A* 

10X40 

1,905,000 

158,750 

7.35 

3-lf* 

4.15 

3-1  A* 

11X22 

610,000 

50,830 

4.97 

5-1" 

2.80 

3-1" 

11X24 

729,000 

60,750 

5.36 

5-1  iV' 

3.03 

3-1" 

11X26 

858,000 

71,500 

5.68 

5-1  A* 

3.21 

3-1  A* 

11X28 

1,002,500 

83,540 

6.02 

4-li" 

3.40 

3-1  A" 

11X30 

1,157,000 

96,420 

6.48 

4-1^" 

3.66 

3-li" 

11X32 

1,325,000 

110,420 

6.65 

3-li" 

3.75 

3-11" 

11X34 

1,500,000 

125,000 

7.07 

3-1  A" 

3.96 

4-1" 

11X36 

1,685,000 

140,420 

7.45 

3-lf" 

4.20 

4-1  rV 

11X38 

1,871,000 

155,920 

7.80 

3-1  ft* 

4.40 

4-1  A* 

11X40 

2,092,000 

174,330 

8.24 

3-1  ft* 

4.65 

4-11" 

11X42 

2,312,500 

192,710 

8.61 

3-lf" 

4.86 

4-11" 

11X44 

2,540,000 

211,670 

8.95 

3-lf" 

5.05 

4-11" 

12X24 

796,000 

66,330 

5.58 

5-1^" 

3.15 

3-1  A" 

12X26 

937,000 

78,080 

6.08 

4-li" 

3.43 

3-1  A* 

12X28 

1,095,000 

91,250 

6.51 

4-1  A* 

3.68 

3-11" 

12X30 

1,262,500 

105,210 

6.97 

4-1  A" 

3.93 

4-1" 

12X32 

1,440,000 

120,000 

7.33 

4-lf" 

4.14 

4-1  A* 

12X34 

1,640,000 

136,670 

7.61 

4-1  A' 

4.30 

4-1  A* 

12X36 

1,841,000 

153,420 

8.12 

3-1  ft* 

4.58 

4-11" 

12X38 

2,032,000 

169,330 

8.42 

3-lf" 

4.75 

4-11" 

12  X40, 

2,249,000 

187,410 

8.92 

3-lf" 

5.03 

5-1" 

DESIGNS    OF    CONCRETE    STRUCTURES  101 

TABLE  la.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

over  central  sup- 

throughout spans. 

Size  of 

Safe  bending 
moment, 
r*  actor  of 

port.     (In  upper 
side  of  girder.) 

(In  lower  side 
of  girder.) 

D63.H1. 

safety  =  3.5. 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

12X42 

2,466,000 

205,490 

9.35 

3-1  If" 

5.28 

6-1  A* 

12X44 

2,683,000 

223,570 

9.85 

3-1  ff" 

5.56 

5-1  A" 

12X46 

2,900,000 

241,670 

10.25 

3-11" 

5.80 

5-1  1" 

12X48 

3,175,000 

264,580 

10.75 

3-11" 

6.08 

5-ll" 

13X26 

1,015,000 

84,580 

6.60 

6-1  A' 

3.73 

5-1" 

13X28 

1,187,500 

98,960 

7.05 

5-1  A" 

3.98 

5-ff" 

13X30 

1,367,500 

115,630 

7.68 

5-lJ" 

4.34 

5-  if" 

13X32 

1,560,000 

130,000 

8.08 

5-1  ^" 

4.57 

5-1" 

13X34 

1,770,000 

147,500 

8.49 

5-1  A* 

4.80 

5-1" 

13X36 

1,995,000 

166,250 

8.92 

4-1}" 

5.04 

5-1" 

13X38 

2,212,500 

184,380 

9.19 

4-1}" 

5.20 

5-1  A" 

13X40 

2,475,000 

206,250 

9.72 

4-1  A" 

5.50 

6-1  A* 

13X42 

2,730,000 

227,500 

10.16 

4-lf" 

5.75 

5-1  J" 

13X44 

3,010,000 

250,830 

10.46 

3-11" 

5.91 

5-1  i" 

13X46 

3,150,000 

262,500 

11.06 

O  I     lj|// 

6.25 

5-lJ" 

13X48 

3,440,000 

287,000 

11.47 

3-1  IS- 

6.48 

5-1  A* 

13X50 

3,770,000 

314,170 

11.98 

3-2" 

6.75 

5-1  A* 

13X52 

4,062,500 

338,540 

12.39 

3-2^" 

6.98 

6-1  A* 

14X28 

1,277,500 

106,460 

7.62 

5-1  ¥ 

4.31 

5-M" 

14X30 

1,472,500 

122,710 

8.20 

5-1  A" 

4.63 

5-1" 

14X32 

1,680,000 

140,000 

8.68 

5-lf 

4.91 

5-1" 

14X34 

1,910,000 

159,170 

8.97 

4-1}" 

5.07 

5-1" 

14X36 

2,145,000 

178,750 

9.48 

4-1  A" 

5.36 

6-1  A* 

14X38 

2,375,000 

197,920 

9.89 

4-lf* 

5.59 

5-1  A" 

14X40 

2,628,750 

219,070 

10.47 

4-1  1" 

5.91 

5-l|" 

14X42 

2,882,500 

240,220 

10.93 

A  1    11 

6.18 

5-l|" 

14X44 

3,136,200 

261,370 

11.42 

4-1  ft* 

6.46 

6-1  A" 

14X46 

3,390,000 

282,500 

11.77 

3-2" 

6.65 

6-1  A* 

14X48 

3,705,000 

308,750 

12.36 

3-2  &" 

6.98 

s-i  A* 

14X50 

4,050,000 

337,500 

12,85 

3-2  ys" 

7.26 

5-11" 

102         HANDBOOK  ON   REINFORCED  CONCRETE. 
TABLE  la.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

Size  of 

Safe  bending 
moment. 

over  central  sup- 
port.    (In  upper 
side  of  girder.) 

throughout  spans. 
(In  lower  side 
of  girder.) 

DOBIu* 

safety  =3.5 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

14X52 

4,375,000 

364,580 

13.27 

3-2f" 

7.50 

5-1}" 

14X54 

4,737,500 

394,790 

13.72 

3-2|" 

7.75 

5-1}" 

14X56 

5,110,000 

425,830 

14.20 

3-2  A" 

8.02 

s-i  A* 

15X30 

1,580,000 

131,800 

8.57 

4-li" 

4.84 

5-1" 

15X32 

1,785,000 

148,750 

8.97 

4-14" 

5.07 

5-1  ^g" 

15X34 

2,047,500 

170,630 

9.62 

4-1  A* 

5.43 

5-1  A' 

15X36 

2,300,000 

191,670 

10.10 

4-lf" 

5.71 

5-  11" 

15X38 

2,550,000 

212,500 

10.54 

4-1  1" 

5.94 

5-1-g" 

15X40 

2,818,750 

234,900 

11.19 

4-1  tt* 

6.32 

5-11" 

15X42 

3,087,500 

257,300 

11.66 

4-1  ft* 

6.59 

5-1  A* 

15X44 

3,356,250 

279,700 

12.18 

4-lf" 

6.88 

5-1  A' 

15X46 

3,625,000 

302,080 

12.75 

4-1  W 

7.21 

5-1}" 

15X48 

3,970,000 

330,830 

13.27 

4-1  }|" 

7.50 

5-1}" 

15X50 

4,337,500 

361,460 

13.84 

3-2i" 

7.82 

5-1}" 

15X52 

4,675,000 

389,580 

14.23 

3-2^" 

8.04 

5-1  A" 

15X54 

5,080,000 

423,330 

14.88 

3-2}" 

8.41 

5-1  A" 

15X56 

5,475,000 

456,250 

15.37 

3-2}" 

8.68 

5-lf" 

15X58 

5,900,000 

491,660 

15.80 

3-2^" 

8.93 

5-lf" 

15X60 

6,300,000 

525,000 

16.23 

3-2f" 

9.17 

5-lf" 

16X32 

1,923,000 

160,250 

9.75 

5-1  A" 

5.51 

5-1  A" 

16X34 

2,180,000 

181,670 

9.84 

5-1  A* 

5.56 

5-1  A* 

16X36 

2,457,500 

204,790 

10.91 

5-1  4" 

6.17 

5-l|* 

16X38 

2,725,000 

227,080 

11.35 

5-14" 

6.42 

5-li" 

16X40 

3,012,500 

251,040 

11.86 

4-lf" 

6.70 

5-1^" 

16X42 

3,300,000 

275,000 

12.38 

4-lf" 

7.00 

5-1  A" 

16X44 

3,582,500 

298,960 

12.97 

4-1  }f" 

7.33 

5-1}" 

16X46 

3,875,000 

322,920 

13.62 

7.70 

5-1}" 

16X48 

4,235,000 

352,920 

14.14 

4-l|" 

8.00 

5-1  A" 

16X50 

4,632,500 

386,040 

14.65 

3-2i» 

8.28 

s-i  A" 

16X52 

5,000,000 

416,670 

15,13 

8.53 

3-1  W 

DESIGNS   OF   CONCRETE    STRUCTURES.          103 
TABLE  la.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

Safe  bending 

over  central  sup- 
port.    (In  upper 

throughout  spans. 
(In  lower  side 

Size  of 

moment. 

side  of  girder.) 

of  girder.) 

safety  =3.5. 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

6X54 

5,415,000 

451,250 

15.65 

3-2  Y$" 

8.83 

3-  ITS" 

6X56 

5,850,000 

487,500 

16.25 

3-2f  " 

9.17 

3-l|  " 

6X58 

6,285,000 

523,750 

16.76 

3-2|  " 

9.46 

3-lif" 

6X60 

6,725,000 

560,420 

17.34 

3-2^ 

9.78 

3-lrT 

6X62 

7,200,000 

600,000 

17.80 

3-2^" 

10.08 

3-1  1  " 

6X64 

7,685,000 

640,420 

18.36 

3-2*  " 

10.38 

3-l|  " 

7X34 

2,315,000 

192,920 

10.90 

5-1*  " 

6.15 

5-1*  * 

7X  36 

2,605,000 

217,080 

11.40 

5-1*" 

6.43 

5-1  rV" 

7X38 

2,895,000 

241,250 

12.04 

5-1  &" 

6.80 

5-1  iV 

7X40 

3,237,500 

269,480 

12.70 

5-lf  " 

7.17 

5-li  " 

7X42 

3,575,000 

298,000 

13.22 

5-lfJ 

7.46 

5-l£  " 

7X44 

3,925,000 

327,080 

13.86 

7.82 

5-li  " 

7X46 

4,110,000 

342,500 

14.40 

4-lp» 

8.13 

4-1  A" 

7X48 

4,500,000 

375,000 

15.00 

8.44 

4-1*  • 

7X50 

4,920,000 

410,000 

15.60 

4-2  *  " 

8.77 

4-1*  • 

7X52 

5,315,000 

442,930 

16.11 

4-2     * 

9.07 

4-1  Tff" 

7X54 

5,760,000 

480,000 

16.85 

4-2^" 

9.48 

4-1  TS" 

7X56 

6,210,000 

517,500 

17.20 

3-2^" 

9.67 

3-  IT!" 

7X58 

6,685,000 

559,080 

17.74 

3-2^" 

9.98 

3~1|  " 

7X60 

7,150,000 

595,830 

18.30 

3-2*  " 

10.35 

3-1&  " 

7X62 

7,650,000 

637,500 

18.88 

3-2*  " 

10.67 

3-1  if" 

7X64 

8,160,000 

680,000 

19.50 

3-2  ]V 

11.03 

3-1  ii" 

7X66 

8,710,000 

725,830 

20.10 

3-2f  " 

11.36 

3-2     " 

7X68 

9,250,000 

770,830 

20.67 

3-2f  " 

11.70 

3-2     * 

8X36 

2,765,000 

230,420 

12.10 

5-1*  " 

6.84 

5-lfV" 

8X38 

3,065,000 

255,420 

12.64 

5-lf  " 

7.13 

5-li  " 

8X40 

3,425,000 

285,420 

13.42 

5-1  W 

7.57 

5-l|  " 

8X42 

3,782,500 

315,210 

14.04 

5-ltt* 

7.93 

5-iA" 

8X44 

4,170,000 

347,500 

14.53 

4-1  if" 

&.  20 

4-1  A" 

8X46 

4,355,000 

362,920 

15.18 

8.56 

4-1*" 

104         HANDBOOK  ON    REINFORCED    CONCRETE 
TABLE  la.  —  Continued. 


1 

2 

3 

4 

5 

6                 7 

Reinforcement 

Reinforcement 

Size  of 
beam. 

Safe  bending 
moment. 
1*  actor  of 

over  central  sup- 
port.    (In  upper 
side  of  girder.) 

throughout  spans. 
(In  lower  side 
of  girder.) 

safety  =3.5 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

18X48 

4,760,000 

396,670 

15.80 

4-2     " 

8.92 

4-1*  " 

18X50 

5,200,000 

433,330 

16.48 

4-2^" 

9.30 

4-1  ft" 

18X52 

5,625,000 

468,750 

17.12 

4-2^  " 

9.65 

4-1  ft" 

18X54 

6,100,000 

508,330 

17.75 

4-2*  " 

10.03 

4-lf  " 

18X56 

6,575,000 

547,920 

18.36 

4-2*  " 

10.37 

4-lf  " 

18X58 

7,075,000 

589,580 

19.00 

4-2ft" 

10.74 

4-lii" 

18X60 

7,565,000 

630,420 

19.36 

s-2ft" 

10.95 

3-1  if" 

18X62 

8,100,000 

675,000 

19.94 

3-2f  " 

11.26 

3-1  W 

18X64 

8,640,000 

720,000 

20.52 

3-2-f  " 

11.59 

3-2     " 

18X66 

9,230,000 

769,170 

21.25 

12.00 

3-2     " 

18X68 

9,785,000 

815,420 

21.84 

3-2^1" 

12.33 

3-2ft" 

18X70 

10,445,000 

870,420 

22.50 

3-2f  " 

12.72 

3-2ft" 

18X72 

11,040,000 

920,000 

23.05 

3-2H" 

13.03 

3-2*" 

19X38 

3,230,000 

269,166 

13.37 

5-1  H" 

7.55 

5-li  " 

19X40 

3,617,500 

301,460 

14.10 

5-lii" 

7.96 

5-1  ft" 

19X42 

3,985,000 

332,080 

14.78 

5-lf  " 

8.35 

5-1  ft" 

19X44 

4,395,000 

367,080 

15.43 

5-lf  " 

8.71 

5-lf  " 

19X46 

4,597,500 

383,130 

16.20 

5-llf" 

9.15 

5-lf  " 

19X48 

5,035,000 

419,580 

16.77 

4-2ft" 

9.48 

4-1  ft" 

19X50 

5,495,000 

457,920 

17.42 

4-21  " 

9.83 

4-lf  " 

19X52 

5,940,000 

495,000 

18.00 

4-2l  " 

10.16 

4-lf  " 

19X54 

6,435,000 

536,250 

18.73 

4-2ft" 

10.57 

4-lf* 

19X56 

6,930,000 

577,500 

19.32 

4-2£  " 

10.90 

19X58 

7,470,000 

622,500 

20.05 

4-2J  " 

11.32 

4-1^" 

19X60 

7,990,000 

665,830 

20.58 

4-2  ft" 

11.61 

4-lf  " 

19X62 

8,560,000 

713,330 

21.10 

3-2^" 

11.91 

3-2     » 

19X64 

9,130,000 

760,830 

21.75 

3-2^" 

12.28 

3-2ft" 

19X66 

9,740,000 

811,670 

22.40 

3-2f  " 

12.65 

3-2ft" 

19X68 

10,350,000 

862,500 

23.00 

3-2  W 

13.00 

3-21  " 

19X70 

11,000,000 

916,670 

23.68 

3-2  If" 

13.37 

3-21  " 

19X72 

11,650,000 

970,830 

24.35 

3-21  " 

13.75 

DESIGNS    OF    CONCRETE    STRUCTURES. 
TABLE  la.  —  Continued. 


105 


1 

2 

3 

4 

5 

6 

7 

Reinforcement 

Reinforcement 

over  central  sup- 

throughout spans. 

Safe  bending 

port.     (In  upper 

(In  lower  side 

Size  of 

moment. 

side  of  girder.) 

of  girder.) 

Deani. 

safety  =  3.5. 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

metal. 

rods. 

metal. 

rods. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

19X74 

12,340,000 

1,028,330 

25.00 

3-2l|" 

14.10 

3-2  &" 

19X76 

13,000,000 

1,083,330 

25.68 

3-2H" 

14.50 

3-2^  " 

20X40 

3,810,000 

317,500 

14.80 

5-lf  " 

8.36 

5-1  A" 

20X42 

4,200,000 

350,000 

15.46 

5-lf  " 

8.73 

5-lf  " 

20X44 

4,627,500 

385,630 

16.20 

5-1  If" 

9.15 

5-  If  " 

20X46 

4,837,500 

403,130 

16.94 

5-lf  " 

9.57 

5-!^" 

20X48 

5,300,000 

441,670 

17.72 

5-1  W 

10.01 

5-1  &" 

20X50 

5,785,000 

482,080 

18.96 

5-1  W 

10.44 

5-4  " 

20X52 

6,250,000 

520,830 

19.02 

5-1  W 

10.76 

5-4  " 

20X54 

6,875,000 

572,920 

19.71 

4-2£  " 

11.14 

4-1  IT 

20  X56 

7,300,000 

608,330 

20.26 

4-2i  " 

11.45 

4-lf  " 

20X58 

7,860,000 

655,000 

21.00 

4-2^" 

11.87 

4-lf  " 

20X60 

8,400,000 

700,000 

21.60 

4-2f  " 

12.20 

4-lf  " 

20X62 

9,000,000 

750,000 

22.32 

4-2f  " 

12.60 

4-  lH" 

20X64 

9,630,000 

802,500 

23.03 

4-2^" 

13.01 

4-1  If" 

20X66 

10,250,000 

854,170 

23.71 

4-2  TO" 

13.40 

4-lf   " 

20X68 

10,875,000 

906,250 

24.15 

3-2|  " 

13.65 

3-2^" 

20X70 

11,600,000 

966,670 

24.95 

3-21T 

14.10 

3-2^* 

20X72 

12,250,000 

10,20,830 

25.60 

3-2  W 

14.47 

3-21  r/ 

20X74 

12,975,000 

1,081,250 

26.22 

3-3     " 

14.82 

3-2^  " 

20X76 

13,700,000 

1,141,670 

26.86 

3-3     " 

15.19 

3-2^  • 

20X78 

14,460,000 

1,205,000 

27.66 

3-3^" 

15.64 

3-2^" 

20X80 

15,240,000 

1,270,000 

28.37 

3-3*  " 

16.01 

3-2^" 

106        HANDBOOK   ON   REINFORCED   CONCRETE. 


KEY  TO  USING  TABLES  IA,  IB,  I,  AND  II. 

In  cases  of  continuous  girders  with  2  spans,  use 
Table  la. 

In  cases  of  continuous  girders  with  3  spans,  use 
Table  Ib. 

In  cases  of  continuous  girders  with  4  or  more 
spans,  use  Table  16,  with  the  modifications  given 
in  the  description  for  Tables  la  and  16. 

In  cases  of  girders  or  beams  with  one  span  only 
supported  at  the  ends,  when  loaded  uniformly, 
and  when  the  span  is  known,  use  Table  II. 

In  cases  of  girders  or  beams  with  one  span  only, 
supported  at  the  ends  and  receiving  concentrated 
loads,  determine  the  maximum  bending  moment, 
and  use  Table  I. 

In  cases  of  girders  or  beams  fixed  at  one  or  both 
ends,  use  Tables  I  and  II,  modified  as  stated  in 
the  note  following  Table  I. 


DESIGNS    OF   CONCRETE   STRUCTURES.          107 
TABLE  16. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 

ment, 

ment, 

intermediate 

intermediate 

outside  spans. 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 

supports.      (In 
upper  side 
of  girder.) 

span. 
(In  lower  side 
of  girder.) 

(In  lower 
side  of 
girder.) 

safety  —  3.5. 

Area 

No.  and 

Area 

No.  anc 

Area 

No.  and 

of 

size  of 

of 

size  of 

of 

size  of 

metal 

bars. 

metal 

bars. 

meta 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in 

Sq.  in 

Sq.  in 

2.5X6 

9,700 

810 

.47 

i-  H" 

.12 

1-f   " 

.38 

1-  f  ^ 

2.5X8 

19,100 

1,600 

.52 

i-f  " 

.13 

i-t7*. 

.42 

2.5X10 

31,600 

2,620 

.65 

i-it" 

.16 

.52 

1-f   " 

2.5X12 

47,200 

3,940 

.66 

i-  it" 

.19 

i-  ^" 

.62 

1-it" 

3X6 

11,700 

975 

.48 

i-f  • 

.12 

i-  1  " 

.38 

1-  f  J 

3X8 

23,050 

1,930 

.59 

i-  it" 

.15 

i-  ^" 

.47 

3X10 

37,500 

3,120 

.66 

i-it" 

.17 

i-  &" 

.53 

1-  f   " 

3X12 

56,900 

4,740 

.78 

i-l" 

.19 

i-  ^" 

.62 

1-   it" 

3X14 

79,400 

6,510 

.88 

i-  if" 

.22 

i-i  " 

.70 

1-1   " 

4X8 

30,600 

2,550 

.75 

i-l  " 

.19 

i-  ^" 

.60 

i-  it" 

4X10 

50,600 

4,220 

.86 

i-  if" 

.21 

1-*;; 

.69 

i-l  " 

4X12 

75,600 

6,300 

.99 

1-1    " 

.25 

.79 

i-  il" 

4X14 

106,000 

8,800 

1.14 

1-1  A" 

.29 

1—    15 

.91 

1-1    " 

4X16 

140,500 

11,740 

1.26 

i-ii  " 

.32 

1-    &" 

1.01 

1-1    " 

5X10 

63,300 

5,280 

1.15 

2-  f   " 

.29 

1-    &" 

.91 

1-1    " 

5X12 

94,500 

7,870 

1.32 

2-   it" 

.33 

1-f    " 

1.06 

1-1  A" 

5X14 

132,000 

11,000 

1.46 

2-  1   " 

.37 

1-f    " 

1.17 

1—1-1-    " 

5X16 

175,600 

14,650 

1.68 

2-   if" 

.42 

i-  \\" 

1.34 

1-1  T3/ 

5X18 

225,000 

18,750 

1.86 

2-1      " 

.47 

i-  W 

1.49 

5X20 

282,000 

23,480 

2.06 

2-1  TJT" 

.52 

1-f" 

1.65 

1-1  ^" 

6X12 

113,600 

9,470 

1.55 

2-  1  " 

.38 

1-f  " 

1.12 

1-1  T3^" 

6X14 

159,000 

13,240 

1.78 

2-   if' 

.45 

1-tt* 

1.42 

2-1  " 

6X16 

210,400 

17,550 

1.97 

2-1     " 

.49 

1-f  " 

1.58 

2—    }5" 

6X18 

271,500 

22,600 

2.19 

2-1  3^" 

.55 

1-f" 

1.75 

2-  if' 

6X20 

338,000 

28,200 

2.40 

2-1** 

.60 

-it" 

1.92 

2-1     " 

6X22 

415,500 

34,690 

2.62 

2—  li-     " 

.65 

-  it" 

2.10 

2-1  T&" 

6X24 

498,500 

41,520 

2.84 

2-l|  " 

.71 

-1" 

2.27 

2-1  iV' 

108 


HANDBOOK   ON    REINFORCED    CONCRETE. 


TABLE  16.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 

ment, 

ment, 

intermediate 

intermediate 

outside  spans. 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 

supports.      (In 
upper  side 
of  girder.) 

span 
(In  lower  side 
of  girder.) 

(In  lower 
side  of 
girder.) 

cofotir   ^    f^ 

&aieiy  —  o.o. 

Area 

No.  am 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

of 

size  of 

metal. 

bars. 

metal 

bars. 

metal. 

bars. 

In. 

In.  Ibs. 

Ft,  Ibs. 

Sq.  in. 

Sq.  in. 

Sq.  in. 

7X14 

185,000 

15,420 

2.14 

3-|  * 

.53 

I-  I" 

1.71 

2-  If" 

7X16 

246,000 

20,550 

2.41 

3-  if" 

.60 

i-  W 

1.93. 

2-1     " 

7X18 

316,000 

26,260 

2.62 

3-  W 

.66 

i-H* 

2.10 

2-1  rV 

7X20 

394,000 

32,800 

2.87 

3-1     " 

.72 

i-l  " 

2.30 

2-1*  " 

7X22 

485,000 

40,400 

3.11 

3-1&" 

.78 

i-tf* 

2.49 

2-11  " 

7X24 

580,000 

48,500 

3.27 

3-lA" 

.82 

i-if" 

2.62 

2-1  iV 

7X26 

685,000 

57,100 

3.53 

3-1&* 

.88 

i-if' 

2.82 

2-liV 

7X28 

800,000 

66,700 

3.77 

3-11  " 

.94 

1-1   " 

3.02 

2-l|  * 

8X16 

281,500 

23,480 

2.63 

3-  W 

.66 

1-M" 

2.10 

2-liV' 

8X18 

360,600 

30,100 

2.90 

3-1     " 

.73 

1-f  " 

2.32 

2-11  " 

8X20 

450,500 

37,600 

3.24 

3-liV' 

.81 

i-iT 

2.59 

3-  if 

8X22 

553,000 

46,150 

3.55 

3-11  " 

.89 

1-1   " 

2.84 

3-1     " 

8X24 

664,000 

55,400 

3.82 

3-11  " 

.96 

1-1   " 

3.06 

3-1     " 

8X26 

781,000 

65,200 

4.09 

3-lfc- 

1.02 

i-iiV' 

3.27 

3-1  ,y 

8X28 

906,000 

75,550 

4.32 

3-lft* 

1.08 

i-iA" 

3.46 

3-11  " 

8X30 

1,050,000 

87,600 

4.65 

3-1}  " 

1.14 

i-4  " 

3.72 

3-11  " 

8X32 

1,202,000 

100,800 

4.97 

3-1  A* 

1.24 

i-ii  " 

3.98 

3-1^ 

9X18 

405,000 

33,750 

3.38 

4-  W 

.85 

i-  W 

2.70 

3-1     " 

9X20 

507,000 

42,250 

3.73 

4-1      " 

.93 

1-1  " 

2.93 

3-1     " 

9X22 

622,000 

52,000 

4.03 

4-1     " 

1.01 

1-1  " 

3.21 

3-iA* 

9X24 

745,000 

62,150 

4.37 

4-lA" 

1.09 

•i-iA" 

3.50 

3-11  " 

9X26 

877,000 

73,150 

4.65 

4-1  h" 

1.16 

i-ii  " 

3.72 

3-11  " 

9X28 

1,000,000 

83,300 

4.73 

3-1}  " 

1.18 

2-  if" 

3.78 

3-11  " 

9X30 

1,185,000 

98,500 

5.22 

3-1  i  " 

1.31 

2-W 

4.17 

4-liV 

9X32 

1,353,000 

112,800 

5.54 

3-lf-  " 

1.39 

2-1" 

4.43 

4-1  rV 

9X34 

1,535,000 

128,000 

5.87 

3-1Y3 

1.47 

2-1" 

4.70 

4-11  " 

9X36 

1,725,000 

143,850 

6.16 

3-1  A" 

1.54 

2-  I  " 

4.93 

4-11  " 

10X20 

564,000 

47,000 

4.10 

4-1     " 

1.03 

2-  I  " 

3.28 

3-1  iY 

10X22 

692,500 

57,750 

4.43 

4-1&" 

1.11 

2-  |   " 

3.  £4 

3-lA" 

DESIGNS    OF   CONCRETE    STRUCTURES. 
TABLE  16.  —  Continued. 


109 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Size 
of 
beam. 

Safe  be 
mom 
Facto 
safety  - 

nding 
ent. 
r  of 

q  c 

Reinforce- 
ment over 
intermediate 
supports.     (In 
upper  side 
of  girder.) 

Reinforce- 
ment, 
intermediate 
span. 
(In  lower  side 
of  girder.) 

Reinforce- 
ment, 
outside  spans. 
(In  lower 
side  of 
girder.) 

—   •>.•>. 

Area 

No,  and 

Area 

No.  and 

Area 

No.  and 

of 

size  of 

of 

size  of 

of 

size  of 

metal. 

bars. 

metal. 

bars. 

metal. 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

Sq.  in. 

10X24 

830,000 

69,200 

4.90 

4-1J  " 

1.23 

*-w 

3.92 

3-l|  " 

10X26 

975,000 

81,250 

5.12 

4-1  1  " 

1.28 

2-  if' 

4.10 

3-l|  " 

10X28 

1,142,000 

95,200 

5.40 

3-lf  " 

1.35 

2-   if" 

4.32 

4-1^" 

10X30 

1,312,000 

109,500 

5.73 

3-1&* 

1.44 

2-  |  " 

4.58 

4-l|  " 

10X32 

1,500,000 

125,000 

6.09 

3-4  " 

1.52 

2-  |   * 

4.87 

4-li  " 

10X34 

1,707,000 

142,200 

6.71 

3-4  " 

1.68 

2-.il" 

5.37 

4-1  iV 

10X36 

1,914,000 

159,600 

6.80 

3-1&* 

1.70 

2-  W 

5.45 

4-1  h" 

10X38 

2,127,000 

177,400 

7.14 

3-1  A" 

1.79 

2-1      " 

5.71 

4-l|  " 

10X40 

2,380,000 

198,500 

7.35 

3-1  1  " 

1.84 

2-1      " 

5.88 

4-li  " 

11X22 

752,000 

63,500 

4.97 

5-1      " 

1.24 

2-  if" 

3.98 

4-1      " 

11X24 

910,000 

75,800 

5.36 

5-liV' 

1.34 

2-  if" 

4.29 

4-1^" 

11X26 

1,074,000 

89,200 

5.68 

5-lTV' 

1.42 

2-1  " 

4.55 

4-1^" 

11X28 

1,253,000 

104^500 

6.02 

4-11  " 

1.51 

2-1   " 

4.82 

4-11  » 

11X30 

1,447,000 

120,500 

6.48 

4-1^  " 

1.62 

2-W 

5.18 

5-1A" 

11X32 

1,655,000 

138,000 

6.65 

3-lJ  " 

1.66 

*•  if* 

5.32 

5-1^" 

11X34 

1,875,000 

156,000 

7.07 

3-lA" 

1.77 

2-  it" 

5.65 

5-li  " 

11  X36 

2,106,000 

175,500 

7.45 

3-lf  " 

1.87 

2-1      " 

5.96 

5-l|  " 

11X38 

2,340,000 

194,600 

7.80 

3-1  W 

1.95 

2-1      " 

6.25 

5-1%  " 

11X40 

2,615,000 

217,500 

8.24 

3-1  W 

2.06 

2-lA" 

6.60 

4-iA" 

11X42 

2,890,000 

240,800 

8.61 

3-l|  " 

2.15 

2-liV' 

6.89 

4-1  h" 

11X44 

3,170,000 

264,000 

8.95 

3-lf  " 

2.24 

2-lTV' 

7.16 

4-l|  » 

12X24 

994,000 

82,800 

5.58 

5-1** 

1.40 

2-|" 

4.47 

4-lTV' 

12X26 

1,170,000 

97,500 

6.08 

4-4  " 

1.52 

2-  1  " 

4.87 

4-1  \  " 

12X28 

1,370,000 

114,000 

6.51 

4-ltk" 

1.63 

2-  if' 

5.21 

5-1^" 

12X30 

1,578,000 

131,500 

6.97 

4-1A" 

1.74 

2-  W 

5.57 

5-1  Ty 

12X32 

1  ,800,000 

150,000 

7.33 

4-1  1  " 

1.83 

2-1      " 

5.87 

5-4  " 

12X34 

2,050,000 

170,700 

7.61 

4-l^c" 

1.90 

2-1      " 

6.10 

5-1*  * 

12X36 

2,300,000 

191,600 

8.12 

3-1  W 

2.03 

2-1      " 

6.49 

5-1  A" 

12X38 

2,540,000 

211,500 

8.42 

3-1  1  " 

2.10 

2-1^" 

6.73 

4-1A" 

110  HANDBOOK   ON    REINFORCED   CONCRETE. 

TABLE  Ib.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 

ment, 

ment, 

intermediate 

intermediate 

outside  spans. 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 

_,0r_i.    r  o  C 

supports.      (In 
upper  side 
of  girder.) 

span. 
(In  lower  side 
of  girder.) 

(In  lower 
side  of 
girder.) 

saiety  —  «>.o. 

Area 

No.  ant 

Area 

No.  anc 

Area 

No.  and 

of 

size  of 

of 

size  of 

of 

size  of 

metal 

bars. 

metal 

bars. 

meta! 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in 

Sq.  in 

Sq.   in 

12X40 

2,816,000 

234,000 

8.92 

3-lf' 

2.23 

2-1A' 

7.13 

4-lf  " 

12X42 

3,080,000 

256,400 

9.35 

3-1  W 

2.34 

2-1!  ' 

7.48 

4-11   " 

12X44 

3,352,000 

279,000 

9.85 

3-1  W 

2.46 

2-li' 

7.88 

4-1  A" 

12X46 

3,620,000 

301,700 

10.25 

3-11  " 

2.56 

3-  if' 

8.20 

4-1  A* 

12X48 

3,970,000 

332,000 

10.75 

3-l|  " 

2.70 

3-1     ' 

8.60 

4-1  \  " 

13X26 

1,270,000 

105,800 

6.60 

5-lfe" 

1.65 

2-  If" 

5.28 

5-1  rV 

13  X28 

1,484,000 

124,000 

7.05 

5-1  A" 

1.76 

2-1     " 

5.65 

5-1  iV 

13X30 

1,710,000 

142,500 

7.68 

5-li  " 

1.92 

2-1     " 

6.15 

5-4  * 

13X32 

1,950,000 

162,500 

8.08 

5-1  A* 

2.02 

2-1      " 

6.47 

5-11  " 

13X34 

2,214,000 

184,400 

8.49 

5-1  A" 

2.12 

2~!  A" 

6.80 

5-11  " 

13X36 

2,493,000 

207,700 

8.92 

4-l|  * 

2.23 

2-1  A" 

7.14 

4-lf  " 

13X38 

2,767,000 

230,200 

9.19 

4-4  " 

2.40 

2-1  1  " 

7.36 

4-lf   " 

13X40 

3,095,000 

258,000 

9.72 

4-1  A" 

2.43 

2-lJ  " 

7.78 

4-1  A* 

13X42 

3,413,000 

284,300 

10.16 

4-lf  " 

2.54 

3-  if" 

8.14 

4-1  T7/ 

13X44 

3,765,000 

313,800 

10.46 

3-11  " 

2.61 

3-  if" 

8.38 

3-1  ^" 

13X46 

3,940,000 

328,000 

11.06 

3-1  If" 

2.77 

3-1     " 

8.85 

3-lf  " 

13X48 

4,300,000 

358,600 

11.47 

3-1  }f" 

2.87 

3-1     " 

9.17 

3-lf  * 

13X50 

4,710,000 

392,800 

11.98 

3-2     " 

2.99 

3-1     " 

9.58 

3-1  W 

13X52 

5,085,000 

422,500 

12.39 

3-2^" 

3.10 

3-iA* 

9.92 

3-11  " 

14X28 

1,593,000 

133,000 

7.62 

5-lf  " 

1.91 

2-1     " 

6.15 

5-11  " 

14X30 

1,840,000 

152,700 

8.20 

5-1  A" 

2.05 

2-1  TS" 

6.56 

5-1  A" 

14X32 

2,100,000 

174,000 

8.68 

5-lf  " 

2.17 

2-1  A" 

6.95 

5-1  A" 

14X34 

2,385,000 

198,000 

8.97 

4-lJ  " 

2.24 

2-1  A" 

7.18 

4-lf  " 

14X36 

2,680,000 

222,400 

9.48 

4-1  A" 

2.37 

2~4  " 

7.60 

4-lf  " 

14X38 

2,970,000 

246,000 

9.89 

4-lf  " 

2.47 

2-lJ  " 

7.92 

4-lui" 

14X40 

3,282,000 

272,400 

10.47 

4-lf   " 

2.62 

3-  if" 

8.38 

41    7  M 
1  16 

14X42 

3,602,000 

299,000 

10.93 

4-1  W 

2.73 

3-1      " 

8.75 

4-1  \  " 

14  X44 

3,920,000 

324,600 

11.42 

4-1  W 

2.86 

3-1      " 

9.14 

4-1  A" 

14X46 

4,238,000 

349,000 

11.77 

3-2     * 

2.94 

3-1     " 

9.43 

3-lif" 

DESIGNS   OF   CONCRETE   STRUCTURES. 
TABLE  I&.  —  Continued. 


HI 


1 

1 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 
intermediate 

ment, 
intermediate 

ment, 
outside  spans. 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 

supports.      (In 
upper  side 
of  girder.) 

span. 
(In  lower  side 
of  girder.) 

(In  lower 
side  of 
girder.) 

satety  ==  o.5. 

Area 

No.  anc 

Area 

No.  anc 

Area 

No.  and 

of 

size  of 

of 

size  of 

of 

size  of 

metal. 

bars. 

metal 

bars. 

metal 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in 

Sq.  in 

Sq.  in 

14X48 

4,625,000 

381,200 

12.36 

3-2*' 

3.09 

3-1*' 

9.89 

3-1  if" 

14X50 

5,055,000 

417,000 

12.85 

3-2** 

3.21 

3-1*' 

10.29 

3-l|  " 

14X52 

5,465,000 

450,100 

13.27 

3-2*  " 

3.32 

3-1*' 

10.61 

3-l|  " 

14X54 

5,918,000 

487,500 

13.72 

3-2|  " 

3.43 

3-1*' 

10.99 

3-i  if" 

14X56 

6,385,000 

526,500 

14.20 

3-2*" 

3.55 

3-1*' 

11.37 

3-2     " 

15X30 

1,975,000 

165,000 

8.57 

4-11  " 

2.14 

3-1  ' 

6.86 

4-1*" 

15X32 

2,230,000 

186,000 

8.97 

4-11  " 

2.24 

3-f  ' 

7.18 

4-1  1   " 

15X34 

2,560,000 

213,500 

9.62 

4-1*" 

2.41 

3-  if' 

7.70 

4-1  1  " 

15X36 

2,872,000 

239,600 

10.10 

4-lf   " 

2.53 

3-  ir 

8.08 

4-1*" 

15X38 

3,186,000 

266,000 

10.54 

4-lf  * 

2.63 

3-  if' 

8.40 

4-1^   " 

15X40 

3,520,000 

294,000 

11.19 

4-1  W 

2.80 

3-1     ' 

8.95 

4-1*  • 

15X42 

3,860,000 

322,000 

11.66 

4-1  W 

2.92 

3-1     ' 

9.32 

4-1*" 

15X44 

4,195,000 

350,000 

12.18 

4-lf   >' 

3.05 

3-1     ' 

9.74 

4-1*" 

15X46 

4,527,000 

378,000 

12.75 

4-1  if" 

3.19 

3-1*' 

10.20 

4-lf  " 

15X48 

4,960,000 

414,000 

13.27 

4-llf' 

3.32 

3-1*' 

10.60 

4-lH" 

15X50 

5,420,000 

452,000 

13.84 

3-2J  " 

3.46 

3-1*  ' 

11.06 

3-1  if" 

15X52 

5,845,000 

485,000 

14.23 

30  3  M 
~  TG" 

3.56 

3-1*  ^ 

11.37 

3-2     " 

15X54 

6,350,000 

529,500 

14.88 

3-2J  " 

3.72 

11.89 

3-2     " 

15X56 

6,849,000 

570,500 

15.37 

3-2^  " 

3.84 

4-1     " 

12.29 

3-2*" 

15X58 

7,370,000 

615,000 

15.80 

3-2JL" 

3.95 

4-1     " 

12.63 

3-2*" 

15X60 

7,872,000 

656,000 

16.23 

3-2f  " 

4.06 

4-1     " 

12.97 

3-2J  " 

16X32 

2,402,000 

200,000 

9.75 

5-1*" 

2.44 

3-  W 

7.80 

5-1*" 

16X34 

2,724,000 

226,800 

9.84 

5-1*" 

2.46 

3-  if  " 

7.87 

5-1*" 

16X36 

3,070,000 

256,000 

10.91 

5-11  " 

2.73 

3-1     " 

8.73 

5-l|  " 

16X28 

3,402,000 

283,300 

11.35 

5-1  1  " 

2.84 

3-1     " 

9.08 

5-lf  " 

16X40 

3,762,000 

313,500 

11.86 

4-lf  " 

2.97 

3-1     " 

9.48 

4-1  fa" 

16X42 

4,125,000 

343,400 

12.38 

4-lf  * 

3.10 

3-1*" 

9.90 

4-lf  " 

16X44 

4,480,000 

373,500 

12.97 

4-1  H^ 

3.24 

3-1*" 

0.10 

4-lf  * 

16X46 

4,850,000 

403,000 

13.62 

3.41 

3-1*" 

0.60 

4-lf  " 

112 


HANDBOOK   ON    REINFORCED   CONCRETE. 


TABLE  16.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 

ment, 

ment, 

intermediate 

intermediate 

outside  spans 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 

,ety- 

supports.      (In 
upper  side 
of  girder.) 

span. 
(In  lower  side 
of  girder.) 

(In  lower, 
side  of 
girder.) 

Area 

No.  am 

Area 

No.  an 

Area 

No.  and 

of 

size  of 

of 

size  oi 

of 

size  of 

metal. 

bars. 

metal 

bars. 

meta 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.   in 

Sq.  in 

Sq.  in 

16X48 

5,290,000 

440,200 

14.14 

4-lf 

3.54 

3-11 

11.00 

4-1  W 

16X50 

5,790,000 

482,000 

14.65 

3-21' 

3.66 

3-11 

11.70 

3-2     " 

16X52 

6,250,000 

520,500 

15.13 

3-21  f 

3.78 

4-1 

12.1 

3-2     " 

16X54 

6,770,000 

564,000 

15.65 

3-2  iV 

3.91 

4-1      ' 

12.5 

3-2^" 

16X56 

7,310,000 

609,500 

16.25 

3-2|  ' 

4.06 

4-1      ' 

13.0 

3-2^" 

16X58 

7,850,000 

654,900 

16.  7f 

3-2|  ' 

4.19 

4-1  &' 

13.4 

3-21  // 

16X60 

8,400,000 

700,000 

17.34 

4.34 

4-liV 

13.86 

3-21  " 

16X62 

9,000,000 

750,000 

17.80 

3-2  ^j' 

4.45 

4-1  TS' 

14.2 

3-2^" 

16X64 

9,600,000 

800,000 

18.36 

3-21  / 

4.59 

4-11  " 

14.67 

3-27lV' 

17X34 

2,886,000 

241,000 

10.90 

5-1*  ' 

2.73 

3-1     " 

8.72 

5-lf  " 

17X36 

3,258,000 

271,500 

11.40 

5-11  / 

2.85 

3-1     " 

9.12 

5-lf  " 

17X38 

3,620,000 

301,400 

12.04 

5-1  TS' 

3.01 

3-1     " 

9.62 

5-1  J^" 

17X40 

4,040,000 

336,500 

12.70 

5-lf  " 

3.18 

3-1  TS" 

10.15 

5-lJ^" 

17X42 

4,470,000 

372,500 

13.22 

5-lf  * 

3.31 

3-1  TS" 

10.50 

5-1*  " 

17X44 

4,900,000 

408,600 

13.86 

5-1  W 

3.47 

3-1  T&" 

11.09 

5-H  " 

17X46 

5,130,000 

427,500 

14.40 

4-1  W 

3.60 

3-11  " 

11.51 

4-1  f  " 

17X48 

5,620,000 

468,500 

15.00 

4-1  If" 

3.75 

3-1  i  " 

12.00 

4-lf  " 

17X50 

6,140,000 

512,200 

15.60 

4-2      " 

3.90 

4-1      " 

12.47 

4-lif* 

17  X52 

6,635,000 

554,000 

16.11 

4-2      " 

4.03 

4-1      " 

12.88 

4-lyi'' 

17X54 

7,200,000 

600,000 

16.85 

4-2^" 

4.21 

4-1  ^" 

13.48 

4-l|  " 

17X56 

7,750,000 

646,000 

17.20 

3-2^" 

4.30 

4-1  ^" 

13.75 

3-21  // 

17  X58 

8,350,000 

698,500 

17.74 

3-2fG" 

4.44 

4-1  TS" 

14.20 

3-2^" 

17X60 

8,925,000 

744,500 

18.30 

3-2^  " 

4.58 

4-1  1  " 

14.63 

3-2l36" 

17X62 

9,550,000 

796,000 

18.88 

3-2^  " 

4.72 

4-11  » 

15.10 

3-2^  " 

17X64 

10,200,000 

850,000 

19  50 

3-2^" 

4.88 

4-1  1  " 

15.60 

3-2  A* 

17X66 

10,900,000 

907,500 

20.10 

3-2  A" 

5.03 

4-1  ^" 

16.08 

3-2f  " 

17X68 

11,560,000 

962,500 

20.67 

3-2f  " 

5.17 

*-!&* 

16.53 

3-2f  " 

18X36 

3,452,000 

288,000 

12.10 

5-11  // 

3.03 

3-1     " 

9.68 

5-1  Ty 

18X38 

3,828,000 

319,200 

12.64 

5-lf  " 

3.16 

3-1  j^" 

10.11 

5-1^" 

DESIGNS   OF   CONCRETE    STRUCTURES. 


113 


TABLE  16.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 

ment, 

ment, 

intermediate 

intermediate 

outside  spans. 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 
safety  —  3  5 

supports.     (In 
upper  side 
of  girder.) 

span. 
(In  lower  side 
of  girder.) 

(In  lower 
side  of 
girder.) 

Area 

No.  am 

Area 

No.  am 

Area 

No.  and 

of 

size  of 

of 

size  ol 

of 

size  of 

metal. 

bars. 

metal 

bars. 

metal. 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in 

Sq.  in 

18X40 

4,275,000 

356,700 

13.42 

5-1  W 

3.36 

3-1* 

10.74 

5-1** 

18X42 

4,725,000 

394,000 

14.04 

5-1  it' 

3.51 

3-1* 

11.23 

5-lj  " 

18X44 

5,205,000 

434,500 

14.53 

4-ltf' 

3.63 

3-1* 

11.62 

4-1  f  " 

18X46 

5,445,000 

453,500 

15.18 

4-1  le' 

3.80 

3-1* 

12.16 

4.  If  " 

18X48 

5,945,000 

495,500 

15.80 

4-2     ' 

3.95 

4-1     ' 

12.65 

4-1  W 

18X50 

6,500,000 

542,200 

16.48 

4-2x6-' 

4.12 

4-1  115 

13.20 

4-1JT 

18X52 

7,028,000 

586,000 

17.12 

4-2*  ' 

4.28 

IHF 

13.70 

18X54 

7,620,000 

636,000 

17.75 

4-2*' 

4.44 

4—  ITT» 

14.20 

4-lif" 

18X56 

8,210,000 

685,000 

18.36 

4-2*' 

4.59 

4-1*' 

14.69 

4-iif" 

18X58 

8,830,000 

737,000 

19.00 

4-2^-' 

4.75 

4-1*' 

15.20 

4-2     " 

18X60 

9,450,000 

788,000 

19.36 

3-2&' 

4.84 

4-1*' 

15.50 

3~2yC 

18X62 

10,130,000 

843,500 

19.94 

3-2f  ' 

4.99 

4-1*  ' 

15.95 

18X64 

10,800,000 

900,000 

20.52 

3-2f  ' 

5.13 

4-1  T&' 

16.40 

S-2f* 

18X66 

11,550,000 

961,000 

21  .'25 

3-2  i*' 

5.31 

4-liV 

17.00 

3-2  3^" 

18X68 

12,230,000 

1,020,000 

21.84 

3-2.T*' 

5.46 

4-1  1^ 

17.46 

3-2  le  " 

18X70 

13,040,000 

1,089,000 

22.50 

3-2f  " 

5.63 

4-1*' 

18.00 

3-2^  " 

18X72 

13,800,000 

1,150,000 

23.05 

3-2H" 

5.76 

4-1*  " 

18.43 

3-2J  " 

19X38 

4,030,000 

336,200 

13.37 

6-lft* 

3.34 

3-iA* 

10.70 

5-l|  " 

19X40 

4,520,000 

376,900 

14.10 

5-1  1^" 

3.53 

3-1*  " 

11.28 

5-1  &" 

19X42 

4,980,000 

415,000 

14.78 

5-lf  " 

3.70 

3-1*  " 

11.82 

5-1^" 

19X44 

5,495,000 

458,800 

15.43 

5-lf  " 

3.86 

4-1     " 

12.33 

5-lf  " 

19X46 

5,745,000 

478,700 

16.20 

5-1  W 

4.05 

4-1     " 

12.94 

5-lf  " 

19X48 

6,291,000 

524,800 

16.77 

4-2&" 

4.19 

4-1  re" 

13.40 

4-1*  ' 

19X50 

6,855,000 

571,000 

17.42 

4-2*  " 

4.36 

4-1  A" 

13.94 

4-4  " 

19X52 

7,430,000 

618,400 

18.00 

4-2*  " 

4.50 

4-1  re" 

14.40 

4-1  if" 

19X54 

8,038,000 

670,000 

18.73 

4-2^" 

4.68 

4-1      " 

14.97 

A_'I  15^ 

19X56 

8,655,000 

722,000 

19.32 

4-2£  " 

4.83 

4-1*  " 

15.45 

4-2   '" 

19X58 

9,325,000 

777,700 

20.05 

4-2£  " 

5.01 

4-1*  " 

16.03 

4-2     " 

19X60 

9.978,000 

832,500 

20.58 

4-2ft* 

5.15 

5-1  A* 

16.46 

4-2  A* 

19X62 

10,700,000 

892,000 

21.10 

3-2is" 

5.23 

5-1  lV 

16.88 

3-2^" 

114 


HANDBOOK   ON    REINFORCED    CONCRETE. 


TABLE  16.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

Reinforce- 

Reinforce- 

Reinforce- 

ment over 

ment, 

ment, 

intermediate 

intermediate 

outside  spans. 

Size 
of 
beam. 

Safe  bending 
moment. 
Factor  of 

supports.      (In 
upper  side 
of  girder.) 

span. 
(In  lower  side 
of  girder.) 

(In  lower 
side  of 
girder.) 

sfifcty  —  3.5, 

Area 

No.  and 

Area 

No.  am' 

Area 

No.  and 

of 

size  of 

of 

size  of 

of 

size  of 

metal. 

bars. 

metal. 

bars. 

metal  . 

bars. 

In. 

In.  Ibs. 

Ft.  Ibs. 

Sq.  in. 

Sq.  in. 

Sq.   in 

19X64 

11,420,000 

950,000 

21  75 

3-2H" 

5.44 

5-1  h" 

17.40 

3-2iV' 

19X66 

12,180,000 

1,015,000 

22.40 

3-2f  " 

5.60 

5-1  iV' 

17.90 

3-2^  " 

19X68 

12,940,000 

1,088,000 

23.00 

3-2H" 

5.75 

5-11-  " 

18.40 

3-2^  " 

19X70 

13,750,000 

1,145,000 

23.68 

3-2  fi" 

5.92 

5-4  " 

18.94 

3-2JL" 

19X72 

14,565,000 

1,213,000 

24.35 

3-21  " 

6.09 

5-i  i  " 

19.46 

3-2&* 

19X74 

15,420,000 

1,286,000 

25.00 

3-2  ft" 

6.25 

5-l|  " 

20.00 

3-2f   " 

19X76 

16,245,000 

1,353,500 

25.68 

3-2  If" 

6.42 

5-1  b" 

20.53 

3-2|  " 

20X40 

4,770,000 

396,800 

14.80 

5-lf  " 

3.70 

4-1      " 

11.85 

5-1^ 

20X42 

5,250,000 

437,500 

15.46 

5-1  f  " 

3.87 

4-1      " 

12.37 

5-lf  " 

20X44 

5,795,000 

482,000 

16.20 

5-1  W 

4.05 

4-1      " 

12.97 

5-lf  " 

20  X46 

6,050,000 

504,700 

16.94 

5-11  " 

4.24 

4-llV' 

13.56 

5-1  W 

20X48 

6,625,000 

552,000 

17.72 

5-1  W 

4.43 

4-1  A" 

14.19 

5-1  W 

20X50 

7,235,000 

602,800 

18.96 

5-1  jf 

4.61 

4-4  " 

14.77 

5-lf  " 

20X52 

7,820,000 

651,200 

19  02 

5-1  ir 

4.76 

4-4  " 

15.22 

4-2     " 

20X54 

8,600,000 

717,000 

19.71 

4-2^  " 

4.93 

4-li  " 

15.79 

4-2     " 

20X56 

9,126,000 

761,000 

20.26 

4-2|  " 

5.07 

5-1      " 

16.24 

4-2^" 

20X58 

9,828,000 

819,200 

21.00 

4-2&* 

5.25 

5-lA" 

16.81 

4-2Ty 

20X60 

10,500,000 

875,000 

21.60 

4-2|  " 

5  40 

5-liV' 

17.30 

4-21  " 

20X62 

11,250,000 

937,700 

22.32 

4-2f  " 

5.58 

5-1A" 

17.88 

4-21  " 

20X64 

12,040,000 

1,003,000 

23.03 

4-2^" 

5.  70 

5-li  " 

18.44 

4-2A* 

20X66 

12,830,000 

1,067,000 

23.71 

4-2^" 

5.93 

5-11  " 

19.00 

3-2^ 

20X68 

13,600,000 

1,145,000 

24.15 

3-21" 

6.04 

5-l|  " 

19.34 

3-2A* 

20X70 

14,510,000 

1,208,000 

24.95 

3-2  W 

6.24 

5-11  " 

19.98 

3-2f  " 

20X72 

15,340,000 

1,278,000 

25.60 

3-2M" 

6.40 

5-1^ 

20.50 

3-2f  " 

20  X74 

16,250,000 

1,353,000 

26.22 

3-3     " 

6.56 

&-iA* 

21.00 

3-2W 

20X76 

17,140,000 

1,428,000 

26.86 

3-3     " 

6.72 

5-1  A" 

21  50 

3-2H" 

20X78 

18,100,000 

1,508,000 

27.66 

3-3A" 

6.92 

5-1  -h" 

22.14 

3-2f  " 

20X80 

19,090,000 

1,588,000 

28.37 

3-3i  " 

7.09 

5-1}-  " 

22.71 

3-2f  " 

DESIGNS   OF   CONCRETE   STRUCTURES.         115 

DESCRIPTION  OF  TABLE  II. 

This  table  is  inserted  to  be  used  in  a  more 
specific  way  than  Table  I,  in  cases  of  uniform 
loading  where  the  total  live  load  in  tons  uniformly 
distributed  along  the  beam  or  girder  is  known,  as 
well  as  the  span  in  feet.  Only  a  sufficient  number 
of  sizes  are  here  given  to  cover  the  ordinary  load- 
ing met  with  in  practice,  and  such  sizes  are  se- 
lected as  are  capable  of  withstanding  the  severest 
loading  for  a  given  amount  of  material  —  in  other 
words,  the  most  economical  sizes.  It  may  happen 
in  practice  that  certain  local  conditions,  such  as 
want  of  head-room,  etc.,  may  enter  the  case  to  an 
extent  to  prohibit  the  use  of  certain  sizes  here 
given.  For  such  cases  Table  I,  which  is  more 
general  in  scope,  may  be  resorted  to.  Then  again, 
in  certain  particular  cases,  neither  of  the  two 
tables  may  apply.  In  such  instances,  which  can 
Jiappen  only  seldom,  the  designer  may  well  afford 
to  spend  his  time  to  meet  the  special  requirements. 

The  table  in  itself  needs  little,  if  any,  explana- 
tion. Column  1  gives  the  span  in  feet;  column  2 
gives  the  gross  load  in  tons  uniformly  distributed 
along  the  span,  given  in  column  1,  that  the  size, 
designated  above,  will  safely  carry  with  a  factor 
of  safety  of  3.5.  Column  3,  in  a  like  manner, 
gives  the  net  load  after  deducting  the  weight  of 
the  beam  itself. 

Only  one  other  thing  needs  mentioning.  It  may 
be  noticed  that  opposite  two  different  spans  of 


116      HANDBOOK  ON   REINFORCED   CONCRETE. 

each  size,  the  corresponding  loading  is  under- 
scored. This  is  to  show  that  all  spans  lying  be- 
tween the  underscoring  are  the  proper  ones  to  use 
whenever  possible,  for  a  cantilever  loading  only, 
in  order  to  be  certain  that  the  shearing  stress 
brought  to  bear  upon  the  section  will  not  be  ex- 
cessive. (Table  III  takes  into  account  the  design 
to  resist  various  shearing  values.)  It  should  be 
noted  that  the  loading  for  all  spans  above  the 
higher  limit,  designated  by  the  underscoring,  can 
safely  be  used  with  a  cantilever  loading,  but  less 
economically,  because,  for  the  sizes  of  shear  bars 
designated  in  Table  III,  there  will  be  supplied 
more  metal  than  is  necessary  to  withstand  the 
shear,  allowing  the  same  factor  of  safety  of  3.5. 
In  other  words,  above  this  limit,  we  are  designing 
safely,  but  not  as  economically,  as  possible.  At 
the  same  time,  other  sizes  for  the  particular  span 
may  be  selected,  which  will  be  safe  as  well  as 
economical.  On  the  other  hand,  it  is  not  safe  to 
use  the  loading  for  spans  below  the  limit  desig- 
nated by  the  underscoring,  without  increasing  the 
area  of  the  shear  bars  over  the  largest  size  given 
in  Table  III.  In  all  cases,  for  loadings  with  sup- 
ported or  fixed  ends,  the  tables  apply  safely. 


DESIGNS    OF   CONCRETE    STRUCTURES. 


117 


TABLE  II.  —  Beams  and  Girders  (Single  Spans  Supported  at 
Ends). 


24"  > 

(  6" 

zy: 

<8" 

2J"  X 

10" 

2*"X 

12" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

3 

87 

85 

4 
5 

.65 
.52 

.62 
.48 

1.28 
1.02 

1.24 
.97 

2.10 
1.68 

2.05 
1.62 

2.52 

2.44 

6 

.43 

.38 

.85 

.79 

1.40 

1.32 

2.10 

2.01 

7 

.37 

.32 

.73 

.66 

1.20 

1.11 

1.80 

1.69 

8 
9 

.32 

.26 

.64 
.51 

.56 
.49 

1.05 
.93 

.95 

.82 

1.58 
1.40 

1.46 
1.27 

10 
11 

.51 

.42 

.84 
76 

.71 
62 

1.26 
1  14 

1.11 
.97 

12 

.70 

.55 

1.05 

.87 

13 

65 

.49 

.07 

.77 

14 

.90 

.69 

15 

84 

.62 

3"X 

12" 

3"X 

14" 

4"> 

C  14" 

4"X 

16" 

5 

3  03 

2  94 

g 

2  53 

2  42 

3  53 

3  40 

4  69 

4  52 

7 

2.16 

2.03 

3.08 

2.93 

4.02 

3.82 

5.36 

5.13 

8 

1.90 

1.75 

2.65 

2.47 

3.52 

3.29 

4.69 

4.43 

9 
10 
11 
12 

1.69 
1.52 
1.38 
1.26 

1.52 
1.33 
1.17 
1.03 

2.35 
2.12 
1.92 
1.81 

2.15 
1.90 
1.68 
1.55 

3.13 

2.82 
2.56 
2.35 

2.87 
2.53 
2.24 
2.00 

4.17 
3.75 
3.41 
3.13 

3.87 
3.42 
3.05 
2.73 

118 


HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  II.  —  Beams  and  Girders.  —  Continued. 


3"  XI 

2" 

3"X 

14" 

4"X 

14 

4"> 

;16" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 
Net. 

Load 
Gross. 

Load 

Net. 

13 

1.17 

.93 

1.63 

1.34 

2.16 

1.78 

2.89 

2.46 

14 

1.08 

.82 

1.51 

1.20 

2.01 

1.60 

2.68 

2.22 

15 

1.01 

.73 

1.41 

1.08 

1.88 

1.44 

2.50 

2.00 

16 

1.32 

.97 

1.76 

1.29 

2.35 

1.82 

17 

1  24 

87 

1  66 

1   17 

2  21 

1   65 

18 

1.18 

.79 

1.56 

1.04 

2.09 

1.49 

19 

1  98 

1   35 

20 

1.88 

1.22 

5"X 

16" 

5"X 

18" 

5"X 

20" 

6"X 

20" 

7 

6.69 

6.40 

8 

5.86 

5.53 

7.50 

7.12 

9.40 

8.98 

11.27 

10.77 

9 

5.20 

4.82 

6.47 

6.05 

8.34 

7.87 

10.04 

9.48 

10 

4.68 

4.26 

6.00 

5.53 

7.52 

7.00 

9.02 

8.39 

11 

4.26 

3.80 

5.46 

4.94 

6.84 

6.26 

8.21 

7.52 

12 

3.95 

3.45 

5.01 

4.45 

6.26 

5.63 

7.52 

6.77 

13 

3.61 

3.07 

4.62 

4.01 

5.78 

5.10 

6.95 

6.13 

14 

3.35 

2.77 

4.30 

3.65 

5.37 

4.64 

6.45 

5.51 

15 

3.13 

2.50 

4.00 

3.30 

5.01 

4.23 

6.02 

5.08 

16 

2.93 

2.26 

3.76 

3.01 

4.70 

3.86 

5.64 

4.64 

17 

2.76 

2.05 

3.53 

2.73 

4.42 

3.58 

5.31 

4.25 

18 

2.61 

1.86 

3.34 

2.50 

4.18 

3.24 

5.02 

3.89 

19 

2.47 

1.68 

3.16 

2.27 

3.96 

2.97 

4.75 

3.56 

20 

2.34 

1.51 

3.00 

2.06 

3.76 

2.71 

4.52 

3.27 

21 

2  86 

1  88 

3  58 

2  48 

4  30 

2  98 

22 

2.78 

1.71 

3.41 

2.26 

4.10 

2.72 

23 



2.61 

1.48 

3.27 

2.07 

3.93 

2.49 

24 

3  13 

1.87 

3.76 

2.26 

25 

3.00 

1.69 

3.61 

2.04 

DESIGNS    OF    CONCRETE    STRUCTURES.          119 
TABLE  II.  —  Beams  and  Girders.  —  Continued. 


6"X 

22" 

6"X 

24" 

7"X 

24" 

7"X 

26" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

9 

12.30 

11.78 

10 

11.08 

10.39 

13.37 

12.62 

15.48 

14.62 

18.25 

17.30 

11 

10.07 

9.31 

12.16 

11.33 

14.08 

13.12 

16.60 

15.56 

12 

9.22 

8.39 

11.15 

10.25 

12.90 

11.85 

15.20 

14.06 

13 

8.52 

7.62 

10.30 

9.32 

11.90 

10.76 

14.04 

12.81 

14 

7.90 

6.93 

9.55 

8.50 

11.05 

9.83 

13.04 

11.71 

15 

7.38 

6.34 

8.91 

7.78 

10.32 

9.31 

12.17 

10.75 

16 

6.92 

5.81 

8.37 

7.17 

9.67 

8.27 

11.41 

9.89 

17 

6.52 

5.35 

7.87 

6.59 

9.10 

7.61 

10.73 

9.12 

18 

6.15 

4.91 

7.43 

6.08 

8.60 

7.02 

10.14 

8.43 

19 

5.83 

4.52 

7.04 

5.61 

8.13 

6.47 

9.62 

7.75 

20 

5.54 

4.16 

6.68 

5.18 

7.73 

5.98 

9.12 

7.22 

21 

5.27 

3.82 

6.38 

4.80 

7.38 

5.54 

8.70 

6.71 

22 

5.03 

3.51 

6.08 

4.43 

7.03 

5.10 

8.30 

6.21 

23 

4.82 

3.23 

5.82 

4.09 

6.73 

4.72 

7.94 

5.76 

24 

4.61 

2.95 

5.58 

3.78 

6.45 

4.35 

7.61 

5.33 

25 

4.43 

2.70 

5.35 

3.47 

6.19 

4.00 

7.30 

4.92 

26 

4.26 

2.46 

5.14 

3.19 

5.97 

3.50 

7.02 

4.55 

27 

4.10 

2.23 

4.95 

2.92 

5.73 

3.37 

6.77 

4.21 

28 

4.78 

2.68 

5.53 

3.08 

6.52 

3.86 

29 

4  61 

2  43 

5  34 

2  80 

6.30 

3  54 

30 

4  46 

2  20 

5.16 

2.53 

6.08 

3.13 

31 

5  90 

2  96 

32 

5.70 

2.66 

120 


HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  II.  —  Beams  and  Girders.  —  Continued. 


7"X 

28" 

8"X 

28" 

8"X 

30" 

8"X 

32" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 
Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 
Net. 

a 

11 

19  40 

18  28 

21  95 

20  66 

12 

17  76 

16  53 

20  10 

18  70 

23  35' 

21  85 

13 

16.40 

15.07 

18.57 

17.05 

21.55 

19.93 

24.62 

22.88 

14 

15.20 

13.77 

17.26 

16.63 

20.00 

18.25 

22.85 

20.98 

15 

14.20 

12.67 

16.10 

14.45 

18.67 

16.80 

21.30 

19.30 

16 

13.32 

11.69 

15.10 

13.23 

17.50 

15.50 

20.00 

17.86 

17 

12.54 

10.81 

14.20 

12.22 

16.46 

14.34 

18.82 

16.55 

18 

11.84 

10.01 

13.42 

11.32 

15.56 

13.31 

17.78 

15.38 

19 

11.22 

9.28 

12.71 

10.49 

14.75 

12.37 

16.86 

14.32 

20 

10.65 

8.61 

12.08 

9.74 

14.00 

11.50 

16.00 

13.33 

21 

10.16 

8.02 

11.50 

9.05 

13.33 

10.71 

15.25 

12.45 

22 

9.68 

7.44 

10.97 

8.40 

12.74 

9.99 

14.56 

11.62 

23 

9.27 

6.93 

10.50 

7.81 

12.17 

9.30 

13.92 

10.85 

24 

8.88 

6.44 

10.06 

7.26 

11.68 

8.68 

13.34 

10.14 

25 

8.52 

5.97 

9.66 

6.74 

11.20 

8.08 

12.80 

9.46 

26 

8.20 

5.55 

9.28 

6.24 

10.77 

7.52 

12.30 

8.83 

27 

7.90 

5.15 

8.95 

5.80 

10.37 

7.00 

11.87 

8.27 

28 

7.62 

4.77 

8.63 

5.36 

10.00 

6.50 

11.44 

7.70 

29 

7.35 

4.39 

8.33 

4.94 

9.65 

6.03 

11.04 

7.17 

30 

7.10 

4.04 

8.06 

4.56 

9.34 

5.59 

10.68 

6.68 

31 

6.88 

3.72 

7.78 

4.16 

9.04 

5.16 

10.32 

6.19 

32 

6.66 

3.40 

7.55 

3.81 

8.75 

4.75 

10.00 

5.73 

33 

6.46 

3.10 

7.32 

3.36 

8.48 

4.36 

9.70 

5.30 

34 

6.27 

2.80 

7.10 

3.13 

8.22 

3.97 

9.41 

4.87 

35 

6.10 

2.53 

6.90 

2.81 

7.99 

3.62 

9.15 

4.48 

36 

7  78 

3  28 

8.90 

4.10 

37 

7.54 

2.92 

8.67 

3.74 

38 

8  43 

3.36 

39 

8.21 

3.01 

40 

8  00 

2.67 

DESIGNS   OF   CONCRETE   STRUCTURES.  121 

TABLE  II.  —  Beams  and  Girders.  —  Continued. 


1 

9"  X  32" 

9"  X  34" 

9"  X  36" 

2 

3 

2 

3 

2 

3 

2 

Span. 

Load 
Gross. 

Load 
Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

13 
14 
15 
16 
17 

18 
19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 

31 

'  32 

33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 

27.80 
25.80 
24.08 
22.55 
21.25 

20.05 
19.00 

18.08 
17.20 
16.40 
15.70 
15.08 
14.45 
13.88 
13.37 
12.90 
12.45 

12.03 

11.54 
11.29 

10.94 
10.52 
10.31 
10.04 
9.76 
9.51 
9.25 
9.02 

25.85 
23.70 
21.83 
20.15 
18.70 

29.30 
27.27 
25.55 
24.04 

22.70 
21.52 

20.43 
19.50 
18.59 
17.78 
17.03 
16.36 
15.74 
15.15 
14.52 
14.10 

13.63 

13.20 

12.78 

12.39 
12.04 
11.69 
11.36 
11.06 
10.76 
10.49 
10.23 
9.98 
9.74 

26.97 
24.88 
23.00 
21.33 

19.83 

30.68 

28.72 
27.08 

25.58 
24.22 

23.02 
21.94 
20.92 
20.00 
19.17 
18.40 
17.71 
17.04 
16.45 
15.87 

15.35 

14.84 
14.40 

13.94 
13.54 
13.15 
12.80 
12.44 
12.12 
11.80 
11.50 
11.22 
10.96 
10.70 
10.47 
10.24 

28  .  15 
26.02 
24.21 

22.54 
21.01 



17.30 
16.15 

15.08 
14.05 
13.10 
12.25 
11.48 
10.70 
9.98 
9.32 
8.70 
8.10 

18.49 

17.24 
16.15 
15.08 
14.11 
13.20 
12.37 
11.59 
10.85 
10.06 
9.48 

8.86 

19.64 
18.40 
17.21 
16.12 
15.12 
14.18 
13.32 
12.49 
11.73 
10.98 

10.29 

9.61 
9.00 



7.53 

6.89 
6.49 

5.99 

5.42 
5.06 
4.64 
4.21 
3.71 
3.40 
3.02 

8.26 

7.68 

7.13 
6.62 
6.11 
5.62 
5.16 
4.71 
4.27 
3.86 
3.45 
3.04 

8.37 
7.80 
7.25 
6.73 
6.20 
5.71 
5.22 
4.85 
4.30 
3.88 
3.45 
3.05 
2.64 



122      HANDBOOK   ON    REINFORCED    CONCRETE. 
TABLE  II.  —  Beams  and  Girders.  —  Continued. 


10"  > 

(36" 

10"  > 

;38" 

10" 

K40" 

11"  > 

;40" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 

Gross. 

Load 

Net. 

16 

31.90 

28  90 

35.45 

32.28 

18 

28.35 

24.97 

31.52 

27.66 

35.30 

31.56 

38.75 

34.63 

20 

25.50 

21.75 

28.34 

24.28 

31.75 

27.59 

34.83 

30.25 

22 

23.20 

19.07 

25.80 

21.45 

28.88 

24.30 

31.70 

26.66 

24 

21.27 

17.77 

23.65 

18.90 

26.48 

21.49 

29.05 

23.55 

26 

19.64 

14.77 

21.84 

16.69 

24.46 

18.55 

26.82 

20.67 

28 

18.24 

12.99 

20.28 

14.73 

22.70 

16.87 

24.92 

17.52 

30 

17.00 

11.36 

18.90 

12.95 

21.18 

14.94 

23.24 

16.37 

32 

15.94 

9.94 

17.74 

11.41 

19.86 

13.21 

21.80 

14.48 

34 

15.00 

8.64 

16.70 

9.97 

18.70 

11.63 

20.50 

12.72 

36 

14.18 

7.41 

15.77 

8.65 

17.56 

10.07 

19.39 

11.15 

38 

13.44 

6.31 

14.94 

7.42 

16.72 

8.82 

18.35 

9.65 

40 

12.76 

5.26 

14.20 

6.28 

15.90 

7.58 

17.40 

8.25 

42 

12.16 

4.28 

13.50 

5.19 

15.13 

6.40 

16.60 

7.00 

44 

11.60 

3.35 

12.90 

4.20 

14.44 

5.29 

15.85 

5.79 

46 

12.35 

3.25 

13.81 

4.26 

15.16 

4.54 

48 

11  83 

2  33 

13  24 

3  27 

14  54 

3.56 

50 

12.70 

2.30 

13.95 

2.51 

u*> 

42" 

11"  X 

44" 

12"  > 

<44" 

12"  X 

46" 

18 

42  80 

38  46 

47  05 

42  46 

49  70 

44  85 

20 

38.50 

33.68 

42.35 

37.30 

44.75 

39.25 

48.30 

42.55 

22 

35.02 

29.72 

38.50 

32.95 

40.70 

34.65 

43.86 

37.53 

24 

32.10 

26.32 

35.27 

29.22 

37.30 

30.70 

40.25 

33.35 

26 

29.64 

23.38 

32.58 

26.03 

34.47 

27.32 

37.10 

29.62 

28 

27.54 

20.79 

30.22 

23.17 

32.00 

24.30 

34.52 

26.47 

30 

25.70 

18.47 

28.22 

20.65 

29.82 

21.57 

32.20 

23.58 

32 

24.10 

16.40 

26.44 

18.37 

28.00 

19.20 

30.25 

21.05 

DESIGNS    OF   CONCRETE    STRUCTURES. 


123 


TABLE  II.  —  Beams  and  Girders.  —  Continued. 


11"  X 

42" 

11"  > 

,44" 

12") 

<  44" 

12"  > 

<46" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 
Net. 

34 

22.67 

14.47 

24.90 

16.33 

26.33 

16.98 

28.40 

18.63 

36 

21.41 

12.83 

23.50 

14.43 

24.88 

14.98 

26.80 

16.45 

38 

20.28 

11.13 

22.28 

12.71 

23.53 

12.94 

25.40 

14.46 

40 

19.27 

9.64 

21.15 

11.05 

22.36 

11.36 

24.15 

13.65 

42 

18.35 

8.21 

20.16 

9.56 

21.32 

9.77 

23.00 

10.92 

44 

17.50 

6.90 

19.24 

8.14 

20.34 

8.24 

21.93 

9.28 

46 

16.75 

5.65 

18.40 

6.80 

19.46 

6.82 

20.98 

7.75 

48 

16.06 

4.47 

17.63 

5.53 

18.65 

5.45 

20.10 

6.20 

50 

15.43 

3.27 

16.93 

4.30 

17.87 

4.12 

19.30 

4.90 

52 

14.83 

2.27 

16.27 

3.15 

17.21 

2.91 

18.58 

3.63 

54 

15  67 

3  03 

16  60 

1  75 

17  89 

2  36 

56 

17  26 

1  16 

58 

16.76 

.06 

12"  X 

48" 

13"  X 

48" 

13") 

<50" 

13"  X 

52" 

2Q 

53  00 

47  00 

55  30 

48  80 

22 

48.20 

41.50 

50.28 

43.13 

57.25 

49.80 

61.50 

53.76 

24 

44.20 

37.00 

46.20 

38.40 

52.45 

44.30 

56.40 

47.96 

26 

40.77 

32.97 

42.55 

34.10 

48.45 

39.60 

52.05 

42.91 

28 

37.87 

29.47 

39.54 

30.44 

45.00 

35.52 

48.30 

38.46 

30 

35.30 

26.30 

36.90 

27.15 

42.00 

31.85 

45.15 

34.60 

32 

33.12 

23.50 

34.60 

24.20 

39.33 

28.49 

42.30 

31.05 

34 

31.17 

20.97 

32.57 

21.52 

37.00 

25.48 

39.80 

27.85 

36 

29.42 

18.62 

30.78 

19.08 

34.96 

22.76 

37.60 

24.95 

38 

27.90 

16.50 

29.13 

16.78 

33.12 

20.26 

35.60 

22.25 

40 

26.50 

14.50 

27.70 

14.70 

31.48 

17.93 

33.87 

19.80 

42 

25.20 

12.60 

26.35 

12.70 

29.95 

15.71 

32.22 

17.45 

44 

24.08 

10.88 

25.16 

11.86 

28.60 

13.50 

30.80 

15.33 

46 

23.05 

9.25 

24.07 

9.12 

27.36 

11.78 

29.44 

13.28 

OF  THE: 

*- .-»<-»  i-r\/ 


124       HANDBOOK  ON   REINFORCED   CONCRETE. 
TABLE  II.  —  Beams  and  Girders.  —  Continued. 


12"  > 

(  48" 

13"  X 

48" 

13" 

X  50~ 

13"  X 

52" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

48 

22.10 

7.70 

23.06 

7.46 

26.20 

9  95 

28.20 

11.33 

50 

21.20 

6.20 

22.15 

5.90 

25.18 

8.24 

27.10 

9.54 

52 

20.38 

4.78 

21.30 

4.40 

24.20 

6.60 

26.06 

7.77 

54 

19.63 

3.43 

20.53 

2.98 

23.30 

5.00 

25.10 

6.10 

56 

18.94 

2.14 

19.76 

1.56 

22.47 

3.51 

24.20 

4.54 

58 
60 

18.28 
17.67 

.88 

19.08 
18.47 

.33 

21.72 
21.00 

2.08 
.70 

23.34 

22.58 

2.94 
1.48 

62 

20  30 

21.85 

14"  X 

52" 

14"  > 

(54" 

14" 

<56" 

15"  > 

:  56" 

22 

66.30 

57.96 

24 

60.80 

51  .70 

65.90 

56.47 

71.20 

61.40 

76.00 

65.47 

26 

56.20 

46.36 

60.80 

50.57 

65.70 

55.08 

70.20 

58.80 

28 

52.20 

41.60 

56.50 

45.50 

61.00 

49.55 

65.20 

52.92 

30 

48.70 

37.33 

52.75 

40.90 

57.00 

44.74 

60.80 

47.65 

32 

45.65 

33.53 

49.75 

37.18 

53.35 

40.27 

57.03 

43.00 

34 

42.95 

30.08 

46.50 

33.14 

50.23 

36.30 

53.72 

38.82 

36 

40.60 

26.98 

44.00 

29.85 

47  .  50 

32.80 

50.75 

34.95 

38 

38.43 

24.03 

41.65 

26.72 

44.98 

29.45 

48.00 

31.34 

40 

36.50 

21.36 

39.52 

23.82 

42.70 

26.35 

45.65 

28.61 

42 

34.75 

19.85 

37.65 

21.15 

40.70 

23.54 

43.50 

25.10 

44 

33.20 

16.53 

35.95 

18.67 

38.80 

20.80 

41.50 

22.20 

46 

31.73 

14.33 

34.40 

16.35 

37.13 

18.30 

39.70 

19.52 

48 

30.40 

12.22 

32.95 

14.10 

35.60 

16.00 

38.00 

17.95 

50 

29.22 

10.29 

31.65 

12.01 

34.18 

13.76 

36.50 

14.58 

52 

28.08 

8.41 

30.40 

10.00 

32.82 

11.56 

35.10 

12.22 

54 

27.06 

6.64 

29.28 

8.08 

31.60 

9.52 

33.80 

10.12 

56 

26.08 

4.88 

28.26 

6.26 

30.50 

7.60 

32.60 

8.05 

58 

25.18 

3.23 

27.28 

4.48 

29.42 

5.70 

31.50 

6.08 

60 

24.32 

1.62 

26.37 

2.72 

28.45 

3.90 

30.43 

4.13 

62 

23.53 

.07 

25.50 

1.15 

27.55 

2.25 

29.45 

2.25 

64 

24.70 

26.70 

.55 

28.53 

.45 

DESIGNS  OF  CONCRETE  STRUCTURES.   125 

TABLE  II.  —  Beams  and  Girders.  —  Continued. 


15"  X  58" 

15"  X  60" 

16"  X  60" 

16"  X  62" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 
Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net.' 

24 

82  00 

71  13 

26 

75.80 

64.03 

80.80 

68.62 

86.20 

73.20 

92.40 

78.98 

28 

70.30 

57.63 

75.00 

61.89 

80.00 

66.00 

85.80 

71.34 

30 

65.60 

52.00 

70.00 

53.94 

74.75 

59.75 

80.10 

64.60 

32 

61.50 

47.00 

65.70 

50.70 

70.05 

54.05 

75.10 

58.58 

34 

57.90 

42.50 

61.77 

45.83 

66.00 

49.00 

70.70 

53.15 

36 

54.70 

38.40 

58.40 

41.54 

62.30 

44.30 

66.75 

48.15 

38 

51.80 

34.60 

55.25 

37.45 

59.00 

40.00 

63.20 

43.57 

40 

49.25 

31.15 

52.50 

33.76 

56.00 

36.00 

60.00 

39.35 

42 

46.80 

27.80 

50.00 

30.32 

53.30 

32.30 

57.20 

35.50 

44 

44.75 

24.85 

47.75 

27.13 

51.00 

29.00 

54.65 

31.95 

46 

42.78 

21.95 

45.70 

24.15 

48.75 

25.75 

52.30 

28.55 

48 

41.00 

19.38 

43.75 

21.27 

46.70 

22.70 

50.00 

25.20 

50 

39.40 

16.78 

42.00 

18.58 

44.90 

19.90 

48.00 

22.20 

52 

37.90 

14.35 

40.40 

16.02 

43.15 

17.15 

46.25 

19.41 

54 

36.44 

11.99 

38.90 

13.60 

41.50 

14.50 

44.50 

16.60 

56 

35.20 

10.82 

37.50 

11.25 

40.00 

12.00 

42.90 

14.00 

58 

33.95 

7.70 

36.20 

9.00 

38.70 

9.70 

41.45 

11.50 

60 

32.80 

5.60 

35.00 

6.90 

37.40 

7.40 

40.00 

9.00 

62 

31.74 

3.66 

33.90 

4.87 

36.20 

5.20 

38.80 

6.80 

64 

30.78 

1.78 

32.86 

2.86 

35  08 

3.08 

37.55 

4.50 

66 

29.85 



31.80 

.85 

34.00 

1.00 

36.40 

2.30 

68 

30.92 

33.00 

35.40 

.40 

16"  X  64" 

17"  X  64" 

17"  X  66" 

17"  X  68" 

28 

91.70 

76.78 

97.20 

81.36 

103.70 

87.40 

110.30 

93.50 

30 

85.50 

69.50 

90.75 

73.80 

96.80 

79.30 

103.00 

85.00 

32 

80.25 

63.20 

85.00 

66.90 

90.75 

72.11 

96.50 

77.30 

34 

75.50 

57.40 

80.00 

60.80 

85.30 

65.50 

90.80 

70.40 

36 

71.30 

52.10 

75.60 

55.26 

80.70 

59.70 

85.75 

64.15 

126        HANDBOOK   ON    REINFORCED    CONCRETE. 
TABLE  II.  —  Beams  and  Girders.  —  Continued. 


16"  > 

(  64" 

17"  > 

;  64" 

17"  ) 

<  66" 

17"  > 

<  68" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 

Gross. 

Load 

Net. 

Load 
Gross. 

Load 
Net. 

38 

67.60 

47.34 

71.60 

50.12 

76.45 

54.30 

81.30 

58.50 

40 

64.20 

42  .  88 

68.00 

45.40 

72.60 

49.30 

77.10 

53.10 

42 

61.00 

38.60 

64.75 

41.02 

69.15 

44.65 

73.50 

48.30 

44 

58.30 

34.86 

61.80 

36.92 

66.00 

40.38 

70.20 

43.80 

46 

55.75 

31.25 

59.15 

33.15 

63.10 

36.30 

67.10 

39.50 

48 

53.50 

27.90 

56.70 

29.58 

60.50 

32.50 

64.30 

35.50 

50 

51.35 

24.70 

54.35 

26.30 

58.20 

29.10 

61.75 

31.75 

52 

49.30 

21.60 

52.30 

22.90 

55.80 

25.50 

59.35 

28.15 

54 

47.55 

18.80 

50.40 

19.90 

53.80 

22.34 

57.20 

24.80 

56 

45.80 

15.97 

48.50 

16.85 

51.80 

19.20 

55.15 

21.55 

58 

44.25 

13.33 

46.85 

14.10 

50.05 

16.25 

53.25 

17.45 

60 

42.75 

10.75 

45  .  35 

11.45 

48.35 

12.35 

51.50 

15.50 

62 

41.45 

8.41 

43.85 

8.85 

46.80 

9.68 

49.80 

12.60 

64 

40.15 

6.05 

42.50 

6.30 

45.40 

8.10 

48.25 

9.85 

66 

38.90 

3.70 

41.20 

3.90 

44.00 

5.57 

46.75 

7.15 

68 

37.75 

1.51 

40.00 

1.60 

42.70 

3.10 

45.40 

4.60 

70 

36.70 

38.90 

41.50 

.75 

44.15 

3.15 

72 

40.30 

42.90 

18"  X 

68" 

18"  X 

70" 

18"  X 

72" 

19"  X 

72" 

28 

116  50 

98  65 

30 

108.90 

89.76 

116.50 

96.80 

122.80 

102.53 

129.50 

118.05 

32 

102.00 

81.60 

109.00 

88.00 

115.00 

93.40 

121.50 

98.62 

34 

96.00 

74.30 

102.50 

80.20 

108.40 

85.45 

114.30 

90.00 

36 

90.75 

67.75 

96.90 

73.28 

102.50 

78.20 

108.00 

82.28 

38 

85.90 

61.68 

91.75 

66.82 

96.90 

71.25 

102  .  40 

75.22 

40 

81.60 

56.10 

87.10 

52.85 

92.00 

65.00 

97.10 

68.50 

42 

77.70 

50.90 

83.00 

55.40 

87.60 

59  .  25 

92.50 

62.50 

44 

74.20 

46.15 

79.20 

50.30 

83  .  75 

54  .  05 

88.30 

56.35 

46 

71.00 

41.84 

75.80 

45.60 

80.20 

49.15 

84.50 

51   64 

48 

68.00 

37.40 

72.60 

41.10 

76  80 

44.40 

81.00 

46.70 

DESIGNS    OF    CONCRETE    STRUCTURES. 


127 


TABLE  II.  —  Beams  and  Girders.  —  Continued. 


18"  > 

:  68" 

18"  ; 

<  70" 

18" 

><  72" 

19"  > 

(  72" 

1 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

50 

65.20 

33.30 

69.70 

36.90 

73.70 

39.94 

77.75 

42.00 

52 

62.75 

29.57 

67.00 

32.90 

70.80 

35  .  70 

74.80 

37.00 

54 

60.50 

26.08 

64.70 

29.25 

68.20 

31.72 

72.00 

33.40 

56 

58.25 

24.55 

62.25 

25.47 

65  80 

28.00 

69.40 

29.64 

58 

56.30 

19.30 

60.00 

21.92 

63.50 

24.30 

67.00 

25.50 

60 

54.50 

16.25 

58.10 

18.60 

61.30 

20.80 

64.75 

21.85 

62 

52.65 

13.15 

56.30 

15.60 

59.35 

17.50 

62.70 

18.40 

64 

51.00 

10.22 

54.50 

12.50 

57.50 

14.30 

60.75 

15.00 

66 

49.40 

8.30 

52.80 

9.50 

55.90 

11.40 

58.90 

11.70 

68 

48.00 

4.65 

51.25 

6.55 

54.20 

8.30 

57.20 

8.55 

70 

46.55 

1.88 

49.80 

3.80 

52.70 

5.45 

55.50 

5.50 

72 

45.30 

48.50 

1.25 

51.20 

2.60 

54.00 

2.52 

74 

49.75 

52.50 

19"  > 

C74" 

19"  > 

C76" 

20") 

<  76" 

20"  X 

78" 

30 

137.00 

114.94 

32 

128.60 

105.10 

135.20 

111.02 

142.70 

117.30 

150.70 

124.70 

34 

121.00 

96.00 

127.40 

101.72 

134.20 

107.25 

141.80 

114.20 

36 

114.40 

87.95 

120.40 

93.20 

127.70 

99.15 

134.00 

104.80 

38 

108.40 

80.50 

114.00 

85.30 

120.00 

89.88 

126.80 

95.95 

40 

103  .  00 

73.60 

108.20 

78.00 

114.20 

82.50 

120.50 

88.00 

42 

98.00 

67.12 

103.00 

71.30 

108.70 

75.40 

115.00 

80.90 

44 

93.50 

61.15 

98.50 

65.30 

103.70 

68.82 

109  .  50 

73.75 

46 

89.50 

55.70 

94.00 

59.45 

99.20 

62.75 

104.90 

67.50 

48 

85.80 

50.50 

90.25 

54.00 

95.10 

56.05 

100  .  50 

61.50 

50 

82.25 

45.50 

86.70 

48.95 

91.25 

51.65 

96.40 

55.80 

52 

79.20 

41.00 

83.25 

43.98 

87.80 

46.55 

92.80 

50.55 

54 

76.25 

36.55 

80.20 

39.45 

84.50 

41.75 

89.25 

45.35 

56 

73  .  50 

32.30 

77.30 

35.05 

81.50 

37.15 

86.10 

40.60 

58 

71.00 

28.40 

74.70 

30.95 

78.70 

32.70 

83.10 

36.00 

60 

68.50 

24.40 

72.20 

26.92 

76.00 

28.50 

80.30 

31.55 

62 

66.30 

20.75 

69.80 

22.92 

73.70 

24.55 

77.80 

26.45 

128        HANDBOOK   ON   REINFORCED    CONCRETE. 


TABLE  II.  —  Beams  and  Girders.  —  Continued. 


1 

19"  X  74" 

19"  X  76" 

20"  X  76" 

20"  X  78" 

2 

3 

2 

3 

2 

3 

2 

3 

Span. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

Load 
Gross. 

Load 

Net. 

64 
66 
68 
70 
72 
74 
76 
78 

64.25 
62.30 
60.60 
58.75 
57.20 
55.70 
54.20 

17.25 
13.80 
10.60 
7.25 
4.25 
1.30 

67.75 
65.70 
63.75 
61.80 
60.20 
58.50 
57.00 

19.45 
15.90 
12.40 
8.90 
5.80 
2.60 

71.30 
69.20 
67.20 
65.20 
63.30 
61.70 
60.00 

20.55 
16.92 
13.30 
9.70 
6.30 
3.00 

75.25 
73.00 
70.90 
68.80 
67.00 
65.20 
63.40 
61.80 

23.25 
19.40 
15.65 
11.90 
8.50 
5.05 
1.70 

20"  X  80" 

34 
36 

38 

40 
42 
44 
46 
48 
50 
52 
54 
56 

58 
60 
62 
64 
66 
68 
70 
72 
74 
76 
78 

149.20 
141.00 
133.50 

127.00 
120.80 
115.60 
110.40 
105.60 
101.50 
97.50 
94.00 
90.50 

87.50 
84.60 
81.80 
79.20 
76.80 
74.60 
72.50 
70.50 
68.50 
66.75 
65.00 

120.90 
111.00 
101.90 

93.70 
85.80 
79.00 
72.10 
65.60 
59.90 
54.20 
49.00 
43.90 

39.20 
34.60 
30.20 
25.90 
21.80 
18.00 
14.20 
10.50 
6.90 
3.45 

DESIGNS   OF   CONCRETE   STRUCTURES. 


129 


DESCRIPTION  OP  TABLE  III. 

Table  III  is  given  to  show  how  much  shearing 
force  the  same  size  of  beams,  figured  to  resist 
bending  in  Table  I,  will  resist.  Suppose  a  certain 
size  has  been  selected  from  Tables  I  or  II  to  with- 
stand the  maximum  bending  moment  in  the  case 
at  hand.  Of  course  we  know  the  maximum  shear- 
ing force  in  this  particular  case,  for  this  had  to  be 
determined  before  obtaining  the  maximum  bend- 
ing moment.  Hence,  by  referring  to  Table  III, 
and  opposite  the  size  already  selected,  ascertain 
under  which  of  the  three  columns,  5,  6,  or  7,  the 


SKETCH  1. 


shearing  force  in  question  falls.  As  you  will  note 
by  the  titles  of  these  columns,  column  5  is  figured 
to  use  shear  bars  with  an  aggregate  area  of  cross- 
section  of  .19  square  inches,  column  6  with  an 
area  of  .28  square  inches;  likewise  column  7  of 
.38  square  inches  area. 

These  shear  bars  are  found  upon  the  market  of 
various  designs.  Very  commonly  they  are  in  the 
form  of  a  U-shaped  bar  lettered  "a"  in  Sketch  1, 
which  may  be  inserted  vertically  to  the  horizontal 
axis  of  the  beams,  or  inclined  at  an  angle,  prop- 


130      HANDBOOK   ON    REINFORCED    CONCRETE. 


erly  60  degrees,  with  the  vertical  axis,  and  in 
the  direction  at  right  angles  to  the  lines  of 
shear  cracks,  which  develop  when  a  beam  is 


SKETCH  2. 


tested  to  destruction,  as  may  be  seen  in  cuts  of 
two  tests  shown  in  another  section  on  page  45. 
These  may  be  met  with  in  the  rolled  and  stamped 
section  shown  in  Sketch  2  and  inserted  in  the 
beam  as  shown  in  Sketch  3.  These  are  two  of 
several  patented  shapes,  which  are  used  to  resist 
longitudinal  shear.  Instead  of  making  the  tables 
apply  to  any  of  these  special  shapes,  the  writer 


15-2 


SKETCH  3  SKETCH  4. 

has  taken  a  general  case,  shown  in  Sketch  4,  to 
which  results  any  of  the  patented  shapes  may  be 
applied. 

By  the  aggregate  area  of  shear  bars  just  men- 
tioned, is  meant  the  combined  area  of  the  cross- 
sections  of  bars  lettered  "b"  in  Sketch  4.  Bars 


DESIGNS  OF  CONCRETE  STRUCTURES.    131 

"b"  should  be  placed  at  an  angle  of  60  degrees, 
about  with  the  vertical. 

In  the  tables,  column  1  gives  the  size  of  beams; 
column  2  gives  the  total  area  of  the  size  opposite 
which  it  appears;  column  3  gives  the  area  of 
concrete,  and  4  the  steel  area,  making  up  the 
total  area  under  column  2. 

VERTICAL  SHEAR.  —  In  obtaining  the  values 
under  column  5,  it  was  reasoned  that  the  maxi- 
mum shearing  force,  which  always  happens  at  a 
support,  causes  a  given  strain  upon  the  section  at 
that  point,  which  strain  is  uniform  at  all  points 
of  the  section,  through  the  steel,  as  well  as  through 
the  concrete.  The  value  of  this  strain  was  so 
fixed  that  the  stress  per  square  inch  caused 
thereby,  throughout  the  concrete  section,  was  very 
moderate,  which  always  happens  with  a  concen- 
trated load  in  the  middle  of  the  span  of  a  beam 
supported  at  both  ends.  The  strain  just  referred 
to  was  fixed  at  .0000167  inches,  which,  with  a 
modulus  of  elasticity  of  3,000,000,  gives  a  working 
stress  of  a  1-1^-3  or  a  1-2-4  concrete,  50  pounds 
per  square  inch,  and  a  factor  of  safety  of  7,  calling 
the  ultimate  shearing  stress  350  pounds  per  square 
inch. 

Column  6  was  figured  allowing  the  working 
strain  and  the  stress  caused  thereby  to  be  mod- 
erate, and  is  adapted  to  meet  the  ordinary  cases 
of  a  beam  uniformly  loaded  and  supported  at  the 
ends.  The  working  stress  was  fixed  at  .000025 
inches,  which  in  a  like  manner  means  a  working 


132      HANDBOOK  ON   REINFORCED   CONCRETE. 

stress  of  75  pounds  per  square  inch,  or  a  factor 
of  safety  of  5.25. 

In  a  like  manner  column  7  was  figured  to  be 
adapted  to  general  cases  of  cantilever  loading, 
where  the  maximum  shearing  force,  for  a  given 
maximum  bending  moment,  is  greatest.  In  this 
case  the  strain  was  limited  to  .0000333  inches,  giv- 
ing a  corresponding  working  stress  of  100  pounds 
per  square  inch,  and  a  factor  of  safety  of  3.5. 

Hence  it  may  be  seen  that  column  5  is  generally 
applicable  to  cases  of  concentrated  central  loads 
upon  beams  supported  at  both  ends;  column  6  to 
cases  of  uniform  loading  upon  beams  similarly 
supported;  and  column  7  to  cases  of  cantilever 
loading.  This  adaptation  holds  only  in  a  general 
way,  and  will  not  apply  to  all  cases,  one  of  which 
was  mentioned  under  Table  II. 

To  obtain  any  shearing  force  under  column  5, 
the  area  of  the  concrete  in  square  inches  given 
under  column  3  was  multiplied  by  50  pounds  per 
square  inch,  to  which  force  in  pounds,  was  added 
the  product  of  multiplying  the  area  of  steel  in 
square  inches  under  column  4  by  500  pounds  per 
square  inch,  since  by  applying  a  given  strain  to 
both  concrete  and  steel,  there  is  caused  ten  times 
the  stress  in  the  steel  as  there  is  in  the  concrete. 
In  a  like  manner  the  values  under  columns  6  and  7 
were  obtained  by  using  75  and  100  pounds  per 
square  inch  allowable  stress  for  the  concrete,  and 
the  proportionate  stresses  of  750  and  1,000  pounds 
per  square  inch  for  the  area  of  steel  respectively. 


DESIGNS    OF   CONCRETE    STRUCTURES.        133 

LONGITUDINAL  SHEAR.  —  It  is  a  well  recognized 
fact  that,  in  elastic  beams  undergoing  vertical 
shearing,  there  is  caused  a  corresponding  longi- 
tudinal shear  which  is  greatest  at  the  neutral  axis 
of  the  section  in  question,  and  decreases  at  any 
axis  approaching  either  the  top  or  bottom  of  the 
section.  In  rectangular  shapes,  the  intensity  of 
stress  at  the  neutral  axis  equals  3  X  the  total 
vertical  shearing  force  divided  by  2  X  the  breadth 
of  the  beam  X  the  depth  of  the  beam,  or,  in  the 
characteristic  form, 

* 

Intensity  of  stress  = 


2  on, 

By  applying  this  to  the  values  of  shearing  force 
given  under  columns  5,  6,  or  7,  for  the  breadth 
and  depth  of  beam  given  under  column  1,  we 
obtain  for  an  intensity  of  longitudinal  shearing 
stress  per  square  inch  of  90  pounds  for  column  5, 
135  pounds  for  column  6,  and  180  pounds  for 
column  7.  By  comparing  these  values  with  the 
corresponding  ones  used  as  working  vertical  shear- 
ing stress  per  square  inch,  namely,  50  pounds, 
75  pounds,  and  100  pounds,  you  will  notice  that  a 
given  vertical  shearing  stress  causes  a  longitudinal 
shearing  stress  of  a  magnitude  of  f  of  itself. 
Hence,  without  inserting  a  steel  member  to  reduce 
the  stress  and  help  out  the  concrete  at  the  neutral 
axis  of  the  sections  near  the  supports,  we  are 
reducing  our  working  factors  of  safety  by  45  per 
cent  in  each  case.  In  other  words,  instead  of 


134      HANDBOOK   ON    REINFORCED    CONCRETE. 

having  factors  of  7,  5.25,  and  3.5,  as  we  had  for 
the  three  particular  cases  in  vertical  shear,  we 
have  corresponding  ones  of  but  3.9,  2.92,  and  1.95, 
which  are  not  ample,  and  if  they  were,  wrould  be 
unsatisfactory  to  use,  since  the  general  design 
would  be  weaker  in  some  places  than  others.  To 
relieve  the  concrete  at  this  point,  we  have  only  to 
insert  a  rod  of  an  area  of  ^  of  that  of  the  concrete 
in  the  layer  where  the  width  of  the  layer  is  the 
side  of  the  rod,  and  the  length  is  the  width  of  the 
beam.  See  rod  (7,  Sketch  4,  which  is  the  rod  just 
mentioned,  and  the  shaded  section,  which  repre- 
sents the  concrete.  The  rod  should  be  ^8,  be- 
cause we  have  to  relieve  the  stress  in  the  concrete 
by  45  per  cent,  and  the  effect  of  a  given  area  of 
steel  is  ten  times  that  of  a  like  area  of  concrete. 
By  combining  these  two  ratios,  we  get  •£$  X  §  =  TV 
This  means  for  a  5-inch  wide  beam,  that  rod  C 
should  be  }  inch  square;  for  a  10-inch  wide  beam, 
J  inch  square;  and  for  a  20-inch  wide  beam,  1 
inch  square.  All  intervening  sizes  may  be  graded 
accordingly.  As  this  rod  C  is  not  required  at  the 
middle  of  the  span,  and  is  most  needed  at  the 
ends,  it  may  not  be  continuous,  but  used  at  the 
ends  only,  and  extend  sufficiently  toward  the 
center  to  satisfy  the  designer  that  the  longitudinal 
shearing  stress  beyond  the  limits  of  the  rod  is  not 
excessive. 

It  has  already  been  stated  that  a  given  vertical 
shearing  stress  causes  a  longitudinal  shearing 
stress  of  |  of  itself.  Hence  in  Sketch  5;  if  we  lay 


SUPPORT 


SIDE  ELEVATION  OF  BEAM 


DESIGNS    OF    CONCRETE    STRUCTURES.  135 

off  to  any  scale,  ab  in  a  vertical  line  and  equal  to 
five  parts,  and  be  to  the  same  scale  ^equal  to  nine 
parts,  and  at  right  angles  to  ab,  then  will  the  line 
ac  give  the  magnitude  of  the  resultant  when  di- 
vided into  the  same  units  that  the  other  two 

forces  were  laid  out  to,  and    

also  the  direction  of  action 
of  this  resultant.  The  mag- 
nitude, as  will  be  noted, 
becomes  2.1  times  the  ver- 
tical shearing  stress,  and  the 
direction  of  action  is  inclined 

to  the  vertical  at  an  angle  bac,  the  tangent  of  which 
is  1.8,  which  denotes  an  angle  of  61  degrees.  It 
has  been  remarked  that  the  shear-cracks,  when  a 
beam  is  tested  to  destruction,  occur  along  lines 
making  an  angle  of  about  60  degrees  with  the 
vertical.  The  above  demonstration  goes  to  show 
why  such  is  the  case. 

It  might  have  been  argued,  upon  first  thought, 
that  putting  in  bar  c,  Sketch  3,  could  have  no 
effect  upon  the  longitudinal  shear  and  would  in 
no  wise  help  out  the  concrete  tending  to  shear  in 
a  plane  parallel  with  itself,  but  upon  referring  to 
Sketch  4,  we  see  that  rod  c  will  cut  the  resultant 
line  of  force  ac  at  an  angle  of  29  degrees  and, 
consequently  can  offer  a  component  to  react 
against  the  resultant  ac. 

The  rods  marked  "b"  in  Sketch  4  will  be  suf- 
ficient to  help  out  the  concrete  at  all  axes  except 
the  neutral  axis,  for  the  aggregate  areas  of  these 


136        HANDBOOK   ON    REINFORCED   CONCRETE. 

rods  will,  when  .19  square  inch  area,  and  the 
width  of  beam  20  inches,  which  is  the  limit  of  the 
table,  reduce  the  longitudinal  shearing  stress  by 
10  per  cent,  which  stress  reduces  in  magnitude 
greatly  as  the  top  or  bottom  layers  are  approached. 
Ten  per  cent  increase  over  the  factor  of  safety  of 
3.9  gives  4.3  at  a  layer  just  above  or  below  the 
neutral  axis,  which  is  ample.  Again,  with  an 
aggregate '  area  of  .38  square  inches  for  rods  "b," 
and  with  a  width  of  beam  of  20  inches,  the  shear- 
ing stress  would  be  reduced  19  per  cent,  and  the 
factor  of  safety  at  a  layer  just  either  side  of  the 
neutral  axis  would  be  2.3  at  the  very  least,  and 
undoubtedly  much  more,  which  may  be  ascer- 
tained by  applying  the  formulae  for  longitudinal 
shearing  stress  at  that  layer. 

In  distributing  the  shear  bars  along  the  length 
of  a  beam  or  girder  the  following  suggestion  is 
offered.  Since  the  shearing  stress  per  square  inch 
varies  uniformly  from  zero  at  the  free  end  of  a 
cantilever,  or  at  the  center  between  the  supports 
or  fixed  ends  of  a  beam,  to  a  maximum  at  the  sup- 
ports or  fixed  ends,  the  spacing  of  bars  should 
vary  inversely  and  uniformly.  Because  this  varia- 
tion is  uniform,  it  may  be  represented  by  the  rela- 
tionship of  the  odd  numbers  1,  3,  5,  7,  etc.,  to 
each  other.  With  a  uniformly  distributed  load- 
ing along  the  length  of  the  beam  or  girder,  the 
shearing  stress  per  square  inch  varies  as  the  length 
of  a  cantilever  beam  called  "Z,"  and  as  the  half 
length  also  called  "Z,"  of  a  beam  supported  or 


DESIGNS   OF   CONCRETE    STUCTURES.          137 

fixed  at  the  ends.  Likewise  the  shearing  stress 
varies  indirectly  as  the  depth  of  the  beam  desig- 
nated "d."  Hence  the  shearing  stress  varies  as 

the  ratio  of  -,.  This  value  increases  when  ap- 
proaching the  supports  and  since,  as  stated  before, 
the  spacing  of  bars  decreases,  this  latter  may  be 

represented  by  the  inverse  ratio  or  -j  -  Accord- 
ingly it  is  suggested  to  call  this  ratio  a  fraction  of 
a  foot,  then  express  its  value  in  inches,  thus  giving 
the  location  of  the  first  pair  of  bars  from  the  sup- 
ports or  fixed  ends.  The  location  of  the  next 
pair,  in  a  like  manner,  is  three  times  this  constant 
from  the  first  pair;  likewise  the  third  pair  are 
distant  five  times  this  constant  from  the  second 
pair  and  so  on,  receding  from  the  support. 

NOTE. 

In  dealing  with  continuous  girders,  the  values 
of  the  safe  shearing  forces  given  in  columns  5,  6, 
and  7  of  Table  III,  should  be  modified  as  follows : 

With  '2  spans  decrease  the  values  given  by  12.5 

per  cent. 
With  3  spans  decrease  the  values  given  by  11.0 

per  cent. 
With  4  spans  decrease  the  values  given  by  11.5 

per  cent. 

With  5,  6,  7,  and  8  spans,  decrease  the  values 
given  by  11,3  per  cent. 


138        HANDBOOK   ON   REINFORCED   CONCRETE. 
TABLE  III. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 
of 
beam. 

Area 
of 
concrete. 

Area 
of 
steel. 

Shearing  force  in  tons. 

Area  of 
shear  bars 
0.19  in. 

Area  of 
shear  bars 
0.28  in. 

Area  of 
shear  bars 
0.38  in. 

2.5X6 

15 

14.53 

.47 

.48 

.72 

.96 

2.5X8 

20 

19.48 

.52 

.62 

.93 

1.24 

2.5X10 

25 

24.35 

.65 

.77 

1.16 

1.54 

2.5X12 

30 

29.43 

.66 

.90 

1.35 

1.80 

3X6 

18 

17.52 

.48 

.56 

.84 

1.12 

3X8 

24 

23.41 

.59 

.73 

1.10 

1.47 

3X10 

30 

29.34 

.66 

.90 

1.35 

1.80 

3X12 

36 

35.22 

.78 

1.08 

1.59 

2.15 

3X14 

42 

41.12 

.88 

1.25 

1.87 

2.50 

4X8 

32 

31.25 

.75 

.97 

1.45 

1.94 

4X10 

40 

39.14 

.86 

1.19 

1.79 

2.39 

4X12 

48 

47.01 

.99 

1.43 

2.14 

2.85 

4X14 

56 

54.86 

1.14 

1.66 

2.49 

3.31 

4X16 

64 

62.74 

1.26 

1.86 

2.79 

3.77 

5X10 

50 

48.85 

1.15 

1.51 

2.26 

3.02 

5X12 

60 

58.68 

1.32 

1.80 

2.70 

3.60 

5X14 

70 

68.54 

1.46 

2.08 

3.12 

4.16 

5X16 

80 

78.32 

1.68 

2.38 

3.32 

4.76 

5X18 

90 

88.14 

1.86 

2.67 

4.00 

5.34 

5X20 

100 

97.94 

2.06 

2.97 

4.50 

5.93 

6X12 

72 

70.47 

1.53 

2.14 

3.22 

4.29 

6X14 

84 

82.22 

1.78 

2.50 

3.75 

5.00 

6X16 

96 

94.03 

1.97 

2.84 

4.26 

5.69 

6X18 

108 

105.81 

2.19 

3.20 

4.79 

6.39 

6X20 

120 

117.60 

2.40 

3.54 

5.31 

7.08 

6X22 

132 

129.38 

2.62 

3.89 

5.81 

7.78 

6X24 

144 

141.16 

2.84 

4.24 

6.36 

8.48 

7X14 

98 

95.86 

2.14 

2.94 

4.41 

5.87 

7X16 

112 

109.59 

2.41 

3.34 

5.02 

6.69 

7X18 

126 

123  .  38 

2.62 

3.73 

5.60 

7.48 

DESIGNS    OF    CONCRETE    STRUCTURES. 


139 


TABLE  III.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 
of 
beam. 

Area 
of 
concrete. 

Area 
of 
steel. 

Shearing  force  in  tons. 

Area  of 
shear  bars 
0.19  in. 

Area  of 
shear  bars 
0.28  in. 

Area  of 
shear  bars 
0.38  in. 

7X20 

140 

137.13 

2.87 

4.14 

6.22 

8.29 

7X22 

154 

150.89 

3.11 

4.55 

6.83 

9.10 

7X24 

168 

164.73 

3.27 

4.93 

7.40 

9.87 

7X26 

182 

178.47 

3.53 

5.34 

8.02 

10.69 

7X28 

196 

192.23 

3.77 

5.74 

8.63 

11.50 

8X16 

128 

125.37 

2.63 

3.79 

5.68 

7.57 

8X18 

144 

141.10 

2.90 

4.25 

6.37 

8.51 

8X20 

160 

156.76 

3.24 

4.93 

7.09 

9.46 

8X22 

176 

172.45 

3.55 

5.19 

7.78 

10.40 

8X24 

192 

188  .  18 

3.82 

5.67 

8.50 

11.32 

8X26 

208 

203.91 

4.09 

6.11 

9.18 

12.24 

8X28 

224 

219.68 

4.32 

6.56 

9.85 

13.15 

8X30 

240 

235  .  35 

4.65 

7.04 

10.57 

14.09 

8X32 

256 

251.03 

4.97 

7.52 

11.26 

«  15.04 

9X18 

162 

158.62 

3.38 

4.81 

7.20 

9.62 

9X20 

180 

176.27 

3.73 

5.34 

8.02 

10.68 

9X22 

198 

193.97 

4.03 

5.85 

8.79 

11.71 

9X24 

216 

211.63 

4.37 

6.38 

9.57 

12.77 

9X26 

234 

229.35 

4.65 

6.94 

10.84 

13.79 

9X28 

252 

247.27 

4.73 

7.36 

11.05 

14.73 

9X30 

270 

264.78 

5.22 

7.93 

11.89 

15.85 

9X32 

288 

282.46 

5.54 

8.44 

12.68 

16.89 

9X34 

306 

300.13 

5.87 

8.97 

13.45 

17.94 

9X36 

324 

317.84 

6.16 

9.48 

14.21 

18.97 

10X20 

200 

195.90 

4.10 

5.92 

8.89 

11.85 

10X22 

220 

215.57 

4.43 

6.49 

9.73 

12.99 

10X24 

240 

235.10 

4.90 

7.10 

10.66 

14.21 

10X26 

260 

254.88 

5.12 

7.66 

11.47 

15.31 

10X28 

280 

274.60 

5.40 

8.23 

12.33 

16.43 

10X30 

300 

294  .  27 

5.73 

8.78 

13.20 

17.58 

10X32 

320 

313.91 

6.09 

9.38 

14.04 

18.74 

10X34 

340 

333.29 

6.71 

10.00 

15.01 

20.02 

140 


HANDBOOK   ON   REINFORCED    CONCRETE. 


TABLE  III.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 
of 
beam. 

Area 
of 
concrete. 

Area 
of 
steel. 

Shearing  force  in  tons. 

Area  of 

shear  bars 
0.19  in. 

Area  of 
shear  bars 
0.28  in. 

Area  of 
shear  bars 
0.38  in. 

10X36 

360 

353  .  20 

6.80 

10.53 

15.80 

21.06 

10X38 

380 

372.86 

7.14 

11.10 

16.63 

22.21 

10X40 

400 

392  .  47 

7.53 

11.68 

17.53 

23.39 

11X22 

242 

237.03 

4.97 

7.17 

10.76 

14.34 

11X24 

264 

258  .  64 

5.36 

7.79 

11.71 

15.61 

11X26 

286 

280  .  32 

5.68 

8.43 

12.64 

16.86 

11X28 

308 

301.98 

6.02 

9.05 

13.56 

18.11 

11X30 

330 

323.52 

6.48 

9.70 

14.53 

19.42 

11X32 

352 

345.35 

6.65 

10.29 

15.45 

20.59 

11X34 

374 

366.93 

7.07 

10.94 

16.40 

21.88 

11X36 

396 

388.55 

7.45 

11.58 

17.37 

23.15 

11  X38 

418 

410.20 

7.80 

12.20 

18.33 

24.40 

11X40 

440 

431.76 

8.24 

12.86 

19.29 

25.71 

11X42 

462 

453.39 

8.61 

13.48 

20.23 

26.98 

11X44 

484 

475.05 

8.95 

14.09 

20.91 

28.23 

12X24 

288 

282.42 

5.58 

8.46 

12.69 

16.91 

12X26 

312 

305.92 

6.08 

9.17 

13.79 

18.34 

12X28 

336 

329.49 

6.51 

9.86 

14.79 

19.73 

12X30 

360 

353  .  03 

6.97 

10.57 

15.86 

21.14 

12X32 

384 

376  .  67 

7.33 

11.26 

16.88 

22.50 

12X34 

408 

400  .  39 

7.61 

11.90 

17.86 

23.83 

12X36 

432 

423.88 

8.12 

12.63 

18.94 

25.26 

12X38 

456 

447.58 

8.42 

13.31 

19.96 

26.59 

12X40 

480 

471.08 

8.92 

13.98 

20.99 

28.02 

12X42 

504 

494  .  65 

9.35 

14.69 

22.03 

29.41 

12X^4 

528 

518.15 

9.85 

15.41 

23.14 

30.84 

12X46 

552 

541.75 

10.25 

16.12 

24.14 

32.22 

12X48 

576 

565.25 

10.75 

16.84 

25.23 

33.64 

13X26 

338 

331.40 

6.60 

9.95 

14.90 

19  87 

13X28 

364 

356.95 

7.05 

10.67 

16.00 

21.38 

13X30 

390 

382  .  32 

7.68 

11.47 

17.23 

22.96 

13X32 

416 

407.92 

8.08 

12.22 

18.33 

24.44 

DESIGNS  OF   CONCRETE    STRUCTURES. 


141 


TABLE  III.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 
of 
beam. 

Area 
of 
concrete. 

Area 
of 
steel. 

Shearing  force  in  tons. 

Area  of 
shear  bars 
0.19  in. 

Area  of 
shear  bars 
0.28  in. 

Area  of 

shear  bars 
0.38  in. 

13X34 

442 

433.51 

8.49 

12.95 

19.43 

25.92 

13X36 

468 

459.08 

8.92 

13.70 

20.55 

27.42 

13X38 

494 

484.81 

9.19 

14.40 

21.60 

28.84 

13X40 

520 

510.28 

9.72 

15.20 

22.80 

30.38 

13X42 

546 

535  .  84 

10.16 

15.94 

23.91 

31.87 

13X44 

572 

561.54 

10.46 

16.65 

24.97 

33.31 

13X46 

598 

586.94 

11.06 

17.94 

26.15 

34.88 

13X48 

624 

612.53 

11.47 

18.17 

27.30 

36.36 

13X50 

650 

638.02 

11.98 

18.95 

28.39 

37.89 

13X52 

676 

663.61 

12.39 

19.69 

29.27 

39.38 

14X28 

392 

384.38 

7.62 

11.50 

17.27 

23.03 

14X30 

420 

411.80 

8.20 

12.35 

18.48 

24.69 

14X32 

448 

439.32 

8.68 

13.15 

19.72 

26.32 

14X34 

476 

467.03 

8.97 

13.91 

20.86 

27.84 

14X36 

504 

494  .  52 

9.48 

14.72 

22.08 

29.47 

14X38 

532 

522.11 

9.89 

15.50 

23.25 

31.05 

14X40 

560 

549  53 

10.47 

16.37 

24.54 

32.71 

14X42 

588 

577.07 

10.93 

17.14 

25.73 

34.32 

14X44 

616 

604  .  58 

11.42 

17.98 

26.91 

35.94 

14X46 

644 

632  .  23 

11.77 

18.74 

28.11 

37.50 

14X48 

672 

659.64 

12.36 

19.56 

29.37 

39.16 

14X50 

700 

687  .  15 

12.85 

20.37 

30.57 

40.78 

14X52 

728 

714.73 

13.27 

21.17 

31.73 

42.37 

14X54 

756 

742  .  28 

13.72 

21.95 

32.92 

43.98 

14X56 

785 

770  .  80 

14.20 

22.85 

34.23 

45.64 

15X30 

450 

441.43 

8.57 

13.18 

19.76 

26.36 

15X32 

480 

471.03 

8.97 

13.99 

21.02 

28.04 

15X34 

510 

500.38 

9.62 

14.91 

22.36 

29.83 

15X36 

540 

529.90 

10.10 

15.78 

23.64 

31.55 

15X38 

570 

559.46 

10.54 

16.61 

24.93 

33.25 

15X40 

600 

588.81 

11.19 

17.50 

26.29 

35.04 

15X42 

630 

618.34 

11.66 

18.36 

27.55 

36.75 

15X44 

660 

647.82 

12.18 

19.23 

28.81 

38.48 

142        HANDBOOK    ON   REINFORCED    CONCRETE. 


TABLE  III.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 
of 
beam. 

Area 
of 
concrete. 

Area 
of 
steel. 

Shearing  force  in  tons. 

Area  of 
shear  bars 
0.19  in. 

Area  of 

shear  bars 
0.28  in. 

Area  of 
shear  bars 
0.38  in. 

15X46 

690 

677  .  25 

12.75 

20.09 

30.15 

40.24 

15X48 

720 

706.71 

13.27 

20  .  97 

31.48 

41.97 

15X50 

750 

736.16 

13.84 

21.86 

32.79 

43.73 

15X52 

780 

765  .  77 

14.23 

22.71 

34.09 

45.41 

15X54 

810 

795.12 

14.88 

23.61 

35.43 

47.20 

15X56 

840 

824.63 

15.37 

24.44 

36.67 

48.92 

15X58 

870 

854  .  20 

15.80 

25.30 

37.93 

50.61 

15X60 

900 

883  .  77 

16.23 

26.15 

39.21 

52.31 

16X32 

512 

502  .  25 

9.75 

14.99 

22.50 

29.99 

16X34 

544 

534.16 

9.84 

15.81 

23.69 

31.63 

16X36 

576 

565  .  09 

10.91 

16.87 

25.29 

33.71 

16X38 

603 

596.65 

11.35 

17.74 

26.63 

35.51 

16X40 

640 

628  .  14 

11.86 

18.67 

27.97 

37.34 

16X42 

672 

659  .  62 

12.38 

19.57 

29.37 

39.17 

16X44 

704 

691.03 

12.97 

20.52 

30.64 

41.04 

16X46 

736 

722  .  38 

13.62 

21.45 

32.19 

42.93 

16X48 

768 

753.86 

14.14 

22.34 

33.54 

44.77 

16X50 

800 

785.35 

14.65 

23.31 

34.95 

46.59 

16X52 

832 

816.87 

15.13 

24.19 

36.27 

48.41 

16X54 

864 

848  .  35 

15.65 

25.11 

37.37 

50.25 

16X56 

896 

879.75 

16.25 

26.04 

39.06 

52.12 

16X58 

928 

911.24 

16.76 

26.94 

40.42 

53.94 

16X60 

960 

942.96 

17.04 

27.83 

41.77 

55.67 

16X62 

992 

974  .  20 

17.80 

28.82 

43.18 

57.61 

16X64 

1024 

1005.64 

18.36 

29.72 

44.64 

59.46 

17X34 

578 

567  .  10 

10.90 

16.88 

25.35 

33.81 

17X38 

612 

600  .  60 

11.40 

17.85 

26.79 

35.73 

17X38 

646 

633.96 

12.04 

18.86 

28.26 

37.72 

17X40 

680 

667  .  30 

12.70 

19.88 

29.76 

39.72 

17X42 

714 

700  .  78 

13.22 

20.80 

31.21 

41.65 

17X44 

748 

734.19 

13.86 

21.82 

32.70 

43.64 

17X46 

782 

767  .  60 

14.40 

22.79 

34.15 

45.58 

17X48 

816 

801.00 

15.00 

23.75 

35.66 

47.55 

DESIGNS   OF   CONCRETE    STRUCTURES.         143 


TABLE  III.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 

of 
beam. 

Area 
of 
concrete. 

Area 

of 
steel. 

Shearing  force  in  tons. 

Area  of 
shear  bars 
0.19  in. 

Area  of 
shear  bars 
0.28  in. 

Area  of 
shear  bars 
0.38  in. 

17X50 

850 

834.40 

15.60 

24.75 

37.11 

49.52 

17X52 

884 

867.89 

16.11 

25.75 

38.57 

51.45 

17X54 

928 

911.15 

16.85 

26.97 

39.03 

53.98 

17X56 

962 

944.80 

17.20 

27.90 

41.82 

55.84 

17X58 

996 

978.26 

17.74 

28.90 

43.33 

57.79 

17X60 

1030 

1011.70 

18.30 

29.84 

44.80 

59.74 

17X62 

1064 

1045.12 

18.88 

30.86 

46.31 

61.70 

17X64 

1098 

1078.50 

19.50 

31.83 

49.70 

63.68 

17X66 

1132 

1111.90 

20.10 

32.80 

49.43 

65.65 

17X68 

1166 

1145.33 

20.67 

33.80 

50.75 

67.60 

18X36 

648 

635.90 

12.10 

18.92 

28.39 

37.85 

18X38 

684 

761.36 

12.64 

19.96 

29.89 

39-89 

18X40 

720 

706.58 

13.42 

21.01 

31.54 

42.04 

18X42 

756 

741.96 

14.04 

22.05 

33.07 

44.12 

18X44 

792 

777.47 

14.53 

23.04 

34.58 

46.14 

18X46 

828 

812.82 

15.18 

24.10 

35.81 

48.23 

18X48 

864 

848  .  20 

15.80 

25.15 

37.68 

50.31 

18X50 

900 

883.52 

16.48 

26.22 

39.28 

52.42 

18X52 

936 

918.88 

17.12 

27.27 

40.85 

54.51 

18X54 

972 

954  .  25 

17.75 

28.32 

42.41 

56.59 

18X56 

1008 

989  .  64 

18.36 

29.34 

44.00 

58.66 

18X58 

1044 

1025.00 

19.00 

30.38 

45.  sr 

60.75 

18X60 

1080 

1060.64 

19.36 

31.34 

47.00 

62.71 

18X62 

1116 

1096.06 

19.94 

32.38 

48.58  ' 

64.78 

18X64 

1152 

1131.48 

20.52 

33.40 

50.17 

66.55 

18X66 

1188 

1166.75 

21.25 

34.43 

51.66 

68.98 

18X68 

1224 

1202.16 

21.84 

35.47 

53.24 

71.03 

18X70 

1260 

1237.50 

22.50 

36.53 

54.82 

73.13 

18X72 

1296 

1262.95 

23.05 

37.34 

55.92 

74.67 

19X38 

722 

708.63 

13.37 

21.04 

31.59 

42.12 

19X40 

760 

745.90 

14.10 

22.18 

33.26 

44.35 

19X42 

798 

783  .  22 

14.78 

23.26 

34.93 

46.55 

19X44 

836 

820  .  57 

15.43 

24.35 

36.54 

48.75 

19X46 

874 

857  .  77 

16  23 

25.45 

38.23 

51.01 

19X48 

912 

895  .  23 

16.77 

26.58 

39.87 

53.15 

144      HANDBOOK  ON  REINFORCED  CONCRETE. 


TABLE  III.  —  Continued. 


1 

2 

3 

4 

5 

6 

7 

Size 
of 
beam. 

Area 
of 
beam. 

Area 
of 
concrete. 

Area 
of 
steel. 

Shearing  force  in  tons. 

Area  of 
shear  bars 
0.19  in. 

Area  of 
shear  bars 
0  .  28  in. 

Area  of 
shear  bars 
0.38  in. 

19X50 

950 

932  .  58 

17.42 

27.66 

41.53 

55  .  34 

19X52 

988 

970.00 

18.00 

28.75 

43.13 

57.50 

19X54 

1026 

1007.27 

18.73 

29.82 

44.76 

59.73 

19X56 

1064 

1044.68 

19.32 

30.93 

46.38 

61.90 

19X58 

1102 

1081.95 

20.05 

32.07 

48.08 

64.13 

19X60 

1140 

1119.42 

20.58 

33.09 

49.62 

66.26 

19X62 

1178 

1146.90 

21.10 

34.15 

50.88 

67.90 

19X64 

1216 

1194.25 

21.75 

35.32 

52.92 

70.59 

19X66 

1254 

1231.60 

22  .40 

36.36 

54.55 

72.28 

19X68 

1292 

1269.00 

23.00 

37.35 

55.95 

74.95 

19X70 

1330 

1306  .  32 

23.68 

38.55 

51.27 

77.16 

19X72 

1368 

1333.65 

24.35 

39.39 

59.08 

78.86 

19X74 

1406 

1381.00 

25.00 

40.75 

61.23 

81.55 

19X76 

1444 

1418.32 

25.68 

41.90 

62.83 

83.76 

20X40 

800 

785.20 

14.80 

23.35 

35.03 

46.66 

20X42 

840 

824.54 

15.46 

24.48 

36.72 

48.96 

20X44 

880 

863.80 

16.20 

25.39 

38.08 

51.29 

20X46 

920 

903.06 

16.94 

26.79 

40.22 

53.63 

20X48 

960 

942  .  28 

17.72 

28.48 

41.95 

55.98 

20X50 

1000 

981.04 

18.96 

29.24 

43.87 

58.53 

20X52 

1040 

1020.98 

19.02 

30.25 

45.38 

60.56 

20X54 

1080 

1060  .  29 

19.71 

31.43 

47.14 

62.87 

20X56 

1120 

1099.74 

20.26 

32.56 

48.83 

65.12 

20X58 

1160 

1139.00 

21.00 

33.70 

50.50 

67.45 

20X60 

1200 

1178.40 

21.60 

34.83 

52.25 

69.72 

20X62 

1240 

1217.68 

22.32 

35.98 

53.99 

72.05 

20X64 

1280 

1256.97 

23.03 

37.14 

55.64 

74  37 

20X66 

1320 

1296.29 

23.71 

38.33 

57.44 

76.67 

20X68 

1360 

1335.85 

24.15 

39  44 

59.16 

78.87 

20X70 

1400 

1375.05 

24.95 

40.62 

60.91 

81.23 

20X72 

1440 

1414.40 

25.60 

41.77 

62.60 

83.52 

20X74 

1480 

1453.78 

26.22 

42.85 

64.33 

85.80 

20X76 

1520 

1493.14 

26.86 

44.00 

66.08 

88.09 

20X78 

1560 

1532.34 

27.66 

45.26 

67.92 

90.45 

20X80 

1600 

1571.63 

28.37 

46.33 

69.53 

92.77 

DESIGNS   OF   CONCRETE   STRUCTURES.         145 

DESCRIPTION  OF  TABLE  IV. 

This  table  is  worked  out  for  the  same  cases  as 
was  Table  II,  up  to,  and  including  beams  13  inches 
wide,  with  the  purpose  of  satisfying  the  designer 
that  no  fear  need  be  felt  that  the  design  be  weak 
in  resisting  deflection.  Like  designing  with  steel 
shapes,  little  or  no  attention  need  be  exercised  in 
this  regard,  unless,  in  cases  where  it  is  expressly 
desired  to  obtain  and  retain  a  floor  strictly  level. 
It  was  thought  that  it  was  unnecessary  to  carry 
out  the  table  further,  as  it  may  readily  be  seen 
that  allowing  a  deflection  of  -g-J-g-  of  the  span,  the 
load  causing  this  deflection,  which  is  expressed  in 
tons  uniformly  distributed,  will  be  twice  as  large 
as  will  the  beam  carry  with  a  factor  of  safety  of 
3.5,  as  shown  in  Table  II. 

In  assigning  an  allowable  deflection  of  -g-J-j-  of 
the  span,  when  working  up  the  table,  the  writer 
had  two  things  in  mind:  first,  that  this  is  a  very 
moderate  amount,  and  may  well  be  allowed  for 
floors  carrying  machinery  which  has  to  be  main- 
tained level,  and  in  line,  and  for  floors,  from  the 
underside  of  the  beams  of  which  is  hung  shafting; 
second,  for  the  reason  that,  at  about  this  deflec- 
tion, hair  cracks  begin  to  appear  upon  the  under- 
side of  the  beam  or  girder  extending  up  to  the 
tension  members  through  the  non-reinforced  pro- 
tection for  the  steel.  These  cracks  are  of  the 
very  slightest  importance  when  considered  as  af- 
fecting the  strength  of  the  beam  or  girder,  and 


146        HANDBOOK   ON    REINFORCED    CONCRETE. 

the  only  objections  that  can  be  offered  against 
their  existence  are  the  unsightly  appearance  they 
offer,  and  that  they  render  the  steel  protection 
less  durable  as  a  fire  resisting  medium.  This 
latter,  however,  is  a  matter  of  great  importance, 
and  should  be  kept  well  in  mind  during  the  design. 
The  table  itself  needs  no  other  explanation 

NOTE. 

Make  the  following  modifications  in  the  values 
given  for  safe  uniformly  distributed  loads  given 
under  Table  IV  when  applying  them  to  continuous 
girders : 

With  2  spans  increase  the  values  by  44.6  per  cent. 

With  3  spans  increase  the  values  by  36.0  per  cent. 

With  4  spans  increase  the  values  by  38.3  per  cent. 

With  5  spans  increase  the  values  by  38.0  per  cent. 

With  6,  7,  8,  and  9  spans,  increase  the  values 
by  38.0  per  cent. 


DESIGNS   OF   CONCRETE    STRUCTURES. 


147 


TABLE  IV.  —  Uniformly  Distributed  Load  in  Tons,  Allowing 
a  Safe  Deflection  of  -%^-Q  of  Span,  for  the  Following  Sizes. 


Span. 

2.5X6 

2.5X8 

12.5X10 

2.5X12 

3X  12 

3X  14 

4X14 

4X16 

5 

1.28 

3.36 

6.85 

12.20 

14.40 

6 

.89 

2.34 

4.76 

8.48 

10.00 

16.40 

21.18 



7 

.65 

1.72 

3.50 

6.23 

7.36 

12.05 

15.55 

23.70 

8 

.50 

1.32 

2.68 

4.78 

5.75 

9.23 

12.18 

18.15 

9 

.40 

1.04 

2.12 

3.77 

4.45 

7.04 

9.40 

14.35 

10 

.84 

1.72 

3.05 

3.61 

5.90 

7.62 

11.63 

11 

1.42 

2.53 

2.98 

4.88 

6.30 

9.60 

12 

1.14 

2.03 

2.50 

4.10 

5.29 

8.07 

13 

1.02 

1.81 

2.14 

3.50 

4.51 

6.88 

14 

1.56 

1.84 

3.02 

3.89 

5.93 

15 

1.36 

1.60 

2.63 

3.39 

5.16 

16 

2.31 

2.98 

4.54 

17 

2.04 

2.64 

4.02 

18 

1.82 

2.35 

3.59 

19 

•3.23 

20 

2.91 

Span. 

5X16 

5X18 

5X  20 

6X  20 

6X  22 

6X  24 

7X  24 

7X  26 

7 

31.15 

8 

23.85 

33.50 

48.10 

56.35 

9 

18.90 

26.50 

37.15 

44.50 

50.60 

10 

15.30 

21.40 

30.10 

36.05 

41.00 

62.50 

76.00 

11 

12.60 

17.70 

24.90 

29.78 

33.88 

52.50 

62.75 

80.20 

12 

10.60 

14.90 

20.90 

25.10 

28.50 

44.10 

52.75 

67.35 

13 

9.05 

12.70 

17.80 

21.38 

24.30 

37.63 

45.00 

57.50 

14 

7.79 

10.90 

15.35 

18.38 

20.88 

32.40 

38.75 

49.50 

15 

6.55 

9.52 

13.40 

16.05 

18.23 

28.25 

33.75 

43.13 

16 

6.00 

8.38 

11.75 

14.10 

16.00 

24.83 

29.70 

37.90 

17 

5.28 

7.40 

10.40 

12.50 

14.20 

22.55 

26.25 

33.55 

18 

4.72 

6.62 

9.29 

11.15 

12.68 

19.60 

23.4-> 

29.93 

19 

4.24 

5.94 

8.34 

10.00 

11.38 

17.63 

21.05 

26.90 

20 

3.82 

5.35 

7.53 

9.03 

10.25 

15.90 

19.00 

24.25 

21 

4.87 

6.83 

8.18 

9.30 

14.40 

17.23 

22.00 

22 

4.42 

6.23 

7.45 

8.50 

13.15 

15.70 

20.05 

23 

*4.03 

5.69 

6.78 

7.75 

12.00 

14.35 

18.35 

24 

5.23 

6.28 

7.13 

11  .05 

13.20 

16.85 

25 

4.82 

5.77 

6.55 

10.18 

12.15 

15.50 

26 

6.08 

9.40 

11.25 

14.35 

27 

5.63 

8.73 

10.45 

13.30 

148        HANDBOOK   ON   REINFORCED    CONCRETE. 


TABLE  IV.  —  Uniformly  Distributed  Load.  —  Continued. 


Span. 

5X16 

5X  18 

5X20 

6X20 

6X22 

6X  24 

7X  24 

7X26 

28 

8  10 

9.70 

12.35 

29 

7.55 

9.03 

11.50 

30 

7  05 

8  43 

10  75 

31 

10.08 

32 

9  97 

33 

8  90 

Span. 

7X  28 

8X  28 

8X  30 

8X  32 

9X32 

9X34 

9X36 

12 
13 

84.50 

72  00 

96.96 

82  50 

120  .  00 
102  50 

124  50 

132  75 

14 

62  00 

71  00 

88  25 

107  00 

114  30 

155  00 

15 

54  00 

62  00 

77  00 

93.50 

99.50 

135.00 

149  .  50 

16 

47  50 

54  50 

67  50 

82  00 

87  50 

118  50 

131  50 

17 
18 
19 
20 
21 
22 

42.00 
37.50 
33.75 
30.40 
27.50 
25  13 

48.25 
43.05 
38.60 
34.85 
31.60 
28  83 

59.80 
53  .  35 
48.00 
43.25 
39.20 
35  75 

72.65 
64.75 
58.25 
52.50 
47.60 
43  45 

77.75 
69.20 
62.10 
56.00 
50.75 
46  25 

105.00 
91.50 
84.20 
76.00 
68.85 
62  75 

116.25 
103.75 
93.50 
84.00 
76.30 
69  50 



23 
24 
25 

23.00 
21.13 
19  45 

26.38 
23.70 
22  25 

32.75 
30.05 

27  70 

39.75 
36.50 
33  63 

42.35 
38.90 
35  85 

57.50 

52.75 
48  55 

63.70 
58.50 
53  90 

26 
27 

28 

18.00 
16.70 
15  50 

20.60 
19.13 
17  80 

25.60 
23.75 
22  10 

31.10 

28.85 
26  80 

33.15 
30.75 
28  60 

44.95 

41.75 
38  30 

49.85 
46.20 
42  90 

29 
30 
31 
32 
33 

14.45 
13.50 
12.65 
11.88 
11.15 

16.55 
15.50 
14.50 
13.60 
12.80' 

20.55 
19.20 
18.00 
16.85 
15.90 

25.00 
23.35 
21.85 
20.50 
19.30 

26.60 
24.90 
23.30 
21.87 
20.60 

36.15 
33.75 
31.65 

29.75 
27.95 

40.00 
37.38 
35.00 
32.88 
30.90 

34 

10  50 

12  05 

15  00 

18  20 

19  38 

26  33 

29   13 

35 
36 

9.90 

11.35 

14.13 
13  35 

17.15 
16  20 

18.30 
17  30 

24.83 
23  45 

27.45 
26  00 

37 
38 

12.65 
12.00 

15.35 
14.55 

16.35 
15.50 

22.20 
21.05 

24.55 
23.27 

39 

13  80 

14  73 

20  00 

22  10 

40 
41 

13.13 

14.00 

19.00 

21.00 
20  00 

42 

19  07 

43 

18  18 

44 

17.40 

DESIGNS    OF  CONCRETE    STRUCTURES. 


149 


TABLE  IV.  —  Uniformly  Distributed  Load.  —  Continued. 


Span. 

10X36 

10X38 

10X40 

11X40 

11X42 

11X44 

12X44 

16 
18 
20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 

145.25 
114.70 
92.90 
76.85 
64.60 
55.00 
47.40 
41.30 
36.25 
32.15 
28.65 
25.75 
23.25 
21.08 
19.20 

170.00 
134.00 
108  .  75 
90.00 
75.65 
64.35 
55.60 
48.40 
42.55 
37.65 
33.60 
30.15 
27.20 
24.70 
22.50 
20.60 
18.93 

158.00 
127.75 
105.75 
89.00 
75.65 
65.35 
57.40 
50.00 
44.25 
39.50 
35.50 
32.00 
29.00 
26.43 
24.20 
22.25 
20.50 

173.50 
140.00 
115.50 
97.00 
82.70 
71.40 
62.20 
54.50 
48.40 
43.45 
38.83 
35.00 
31.75 
28.90 
26.45 
24.35 
22.40 

200.00 
162.00 
134.00 
112.75 
96.00 
82.85 
72.15 
63.40 
56.20 
50.00 
45.00 
40.55 
36.80 
33.55 
30.65 
28.20 
26.00 
24.00 

229.00 
206.00 
153.40 
129.00 
110.00 
94.75 
82.50 
72.50 
64.25 
57.30 
51.50 
46.40 
42.10 
38.40 
35.10 
32.25 
29.75 
27.50 
25  .  50 

242.00 
196.00 
162.25 
136.50 
116.25 
100.25 
87.20 
76.70 
67.90 
60.50 
54.35 
49.00 
44.50 
40.60 
37.05 
34.10 
31.40 
29.00 
26.90 



Span. 

12X46 

12X48 

13X48 

13X50 

13X52 

20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 

221.00 
183.00 
153.60 
130.75 
113.00 
98.25 
86.30 
76.50 
68.20 
61.20 
55.20 
50.00 
45.60 
41.75 
38.20 
35.35 
32.70 
30.35 
28.15 

251.25 
207  .  50 
179.90 
148.50 
128.40 
111.90 
98.25 
87.00 
77.50 
69.70 
62.80 
57.00 
52.00 
47.55 
43.65 
40.25 
37.25 
34.50 
32.10 
29.95 

271.50 
224.50 
188.75 
160.50 
138.50 
120.50 
106.00 
94.00 
83.80 
75.15 
67.75 
61.50 
56.15 
51.30 
47.65 
43.45 
40.15 
37.25 
34.60 
32.30 
30.15 

255.00 
215.00 
183.00 
108.00 
137.50 
121.00 
107.00 
95.50 
85.75 
77.35 
70.10 
63.90 
58.50 
53.75 
49.55 
45.80 
42.50 
39.50 
36.85 
34.38 
32.25 

286.50 
240.75 
205.00 
177.00 
154.00 
135.50 
120.00 
107.00 
96.00 
86.50 
79.75 
71.50 
65.50 
60.20 
55.50 
51.25 
47.55 
44.25 
41.25 
38.50 
36.05 



150       HANDBOOK   ON    REINFORCED    CONCRETE. 

DESCRIPTION  OF  TABLE  V. 

This  table  was  prepared  to  serve  the  same 
purpose  in  designing  floors,  as  was  Table  I  in 
designing  beams  and  girders.  All  the  columns  will 
explain  themselves  after  reading  the  description 
of  Table  I. 

The  thickness  of  the  floor  here  given,  includes 
both  the  top  1-inch  wearing  surface  and  1  inch 
below  the  steel  tension  members,  serving  for  a  fire- 
resisting  medium,  as  well  as  a  finish.  In  the 
tables,  neither  of  these  thicknesses  is  considered 
in  obtaining  the  moment  of  resistance  of  the 
^section.  The  wearing  surface  was  not  considered 
for  reasons  stated  in  Part  I,  and,  of  course,  the 
protection  for  the  steel  could  not  be,  because  it 
lies  outside  the  tension  members.  In  this  way, 
2  inches  is  added  to  the  thickness  of  the  floor  from 
which  no  benefit  is  expected  to  resist  the  moment 
caused  by  the  loading,  and  accordingly  as  thick 
a  concrete  floor  results  as  does  a  wooden  one, 
when  figuring  for  deflection,  and  a  thicker  one, 
when  figuring  for  strength.  However,  when  the 
thickness  of  the  top  wooden  floor  is  added,  the 
thickness  of  the  concrete  floor,  for  resisting 
strength,  will  compare  favorably  with  the  wooden 
one.  Finally,  in  the  concrete  one,  we  have 
included  the  thickness  to  render  the  same  fire 
resisting,  and,  for  this  reason,  have  more  than 
offset  any  objections  that  might  be  imposed  re- 
garding space  occupied. 


DESIGNS   OF   CONCRETE    STRUCTURES. 


151 


The  moments  here  given  in  columns  5  and  6 
are  figured,  allowing  a  factor  of  safety  of  3.5, 
which  is  very  ample,  especially  so  when  the  top 
1-inch  wearing  surface  is  considered  as  offering  no 
resistance. 

The  values  of  the  tensile  stress  per  square  inch, 
given  in  column  11,  brought  to  bear  upon  the 
concrete  in  the  tensile  layers,  are  reduced  to  a 
minimum  in  the  case  of  floors  where  the  ratio  of 
the  concrete  resisting  area  to  that  of  the  steel, 
in  the  tensile  layer,  is  a  maximum.  This  must 
necessarily  be  so,  since  the  moment  of  resistance 
of  the  concrete  area  above  the  neutral  axis,  which 
must  withstand  the  moment  of  the  loading  by 
compression,  and  which  varies  as  the  square  of 
the  effective  depth  of  the  section  is,  in  the  case  of 
floors  where  the  depth  is  small,  very  much  less 
for  a  given  resisting  area  of  concrete  in  the  tensile 
layer  than  in  the  case  of  beams  where  the  effective 
depth  for  a  like  resisting  area  is  large. 

For  a  like  reason,  because  the  shearing  force  re- 
sulting from  a  loading  giving  a  limiting  bending 
moment  is,  in  the  case  of  floors,  small  in  compari- 
son with  the  resisting  area,  the  stress  per  square 
inch  produced  throughout  the  section  is  corre- 
spondingly small.  Not  only  this,  but  the  steel 
tension  members  are  located  quite  near  the  neu- 
tral axis,  and  cross  the  lines  of  resultant  shear  at 
an  angle,  and  hence  offer  a  component  to  resist 
the  resultant  shear.  Consequently,  it  was  thought 
unnecessary  to  compute  tables  for  shearing  values 


152        HANDBOOK   ON    REINFORCED    CONCRETE. 

when  failure,  with  ordinary  spans,  always  results 
by  compression  of  the  upper  fibers,  allowing  of 
course,  that  a  sufficient  tensile  moment  of  resis- 
tance has  been  furnished. 


TABLE  V. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

. 

Dis- 

t-, 

£ 

a 

0>     . 

H-i 

o 

a  ® 

£j3 

J2.C 

tance 

ft  . 

S3        o 

®  . 

1| 

L 

o 
Sfia 

ll 

z7 

|| 

ll 

below 
center 

ll 

111 

|| 

o  0 
gg 

<•->    ^i 

H 
g 

1 

1 

per 

foot 
width. 

ll 

j! 

oment  i 
3er  foot 

of 
gravity 
to 
neutral 

F 

•si 
s5 

;ress  in  < 
>er  squa 

ft 

S 

axis. 

<q 

QQ 

< 

36  ~ 

In. 

Lbs. 

Sq.  in. 

In. 

Sq.  in. 

Sq.  in. 

Lbs. 

3.5 

43.8 

42 

4.50 

2,250 

188 

.22 

.27 

i 

4.22 

100 

4 

50 

48 

*  8 

-    4,000 

333 

.27 

.37 

A 

3.87 

142 

4.5 

56.2 

54 

12.8 

6,200 

517 

.25 

'.38 

T$ 

5.40 

104 

5 

62.5 

60 

18 

9,000 

750 

.30 

.50 

% 

5.50 

136 

5.5 

68.7 

66 

24.5 

12,450 

1038 

.37 

.60 

ft 

6.10 

147 

6 

75 

72 

32 

16,000 

1333 

.41 

.73 

f 

6.72 

164 

6.5 

81.2 

78 

40.5 

20,250 

1688 

.45 

.75 

f 

6.72 

168 

7 

87.5 

84 

50 

25,000 

2083 

.47 

.82 

H 

7.30 

168 

7.5 

94 

90 

60.5 

30,250 

2520 

.47 

.89 

H 

7.30 

182 

8 

100 

8ft 

72 

36,000 

3000 

.49 

.94 

T5 

7.30 

193 

8.5 

106.2 

102 

84.5 

42,250 

3520 

.51 

.03 

f 

7.87 

197 

9 

112.5 

108 

98 

49,000 

4083 

.53 

.10 

f 

7.87 

210 

9.5 

118.5 

114 

112.5 

56,250 

4688 

.58 

.18 

it 

8.43 

210 

10 

125 

120 

128 

64,000 

5333 

.58 

.25 

if 

8.43 

222 

10.5 

131.5 

126 

144.5 

72,250 

6020 

.58 

.31 

T6 

8.43 

233 

11 

137.5 

132 

162 

81,000 

6750 

.57 

.39 

1 

8.98 

232 

11.5 

144 

138 

181 

90,500 

7542 

.57 

.44 

8.98 

240 

12 

150 

144 

200 

100,000 

8333 

.58 

.51 

I 

8.98 

252 

DESIGNS  OF  CONCRETE  STRUCTURES.     153 

DESCRIPTION  OF  TABLE  Va. 

The  amount  of  steel  given  in  columns  8  and  9 
of  Table  V  is  needed  to  furnish  the  required 
tensile  resistance,  to  withstand  the  bending  mo- 
ment, and  hence  the  location  of  the  same  should 
be  at  right  angles  to  the  direction  of  the  support- 
ing beams.  Since  the  section  of  steel  just  referred 
to  is  stressed  to  only  16,000  pounds  per  square 
inch,  but  43  per  cent  of  the  section,  provided  the 
same  had  an  elastic  limit  of  37,000  pounds  per 
square  inch,  would  be  required,  and  but  33  per 
cent  of  the  section,  provided  a  steel  with  an  elastic 
limit  of  50,000  pounds  per  square  inch  were  used. 
The  remaining  57  or  67  per  cent  of  the  area  of 
the  steel  corresponding  to  factors  of  safety  of  2.4 
and  3  respectively,  could  be  used  to  overcome  any 
tension  caused  by  an  increase  of  temperature  pro- 
ducing expansion.  As  stated  under  Part  II,  a 
rise  of  temperature  of  70  degrees  F.  would  be  the 
maximum  met  with  in  practice,  and,  as  stated 
there,  to  overcome  this,  requires  about  .6  square 
inch  of  steel  with  an  elastic  limit  of  50,000  pounds 
per  square  inch  per  square  foot  of  concrete.  To 
show  that  the  67  per  cent  of  steel  section  just 
stated  is  sufficient  to  take  the  tension  caused  by 
the  expansion  produced  by  the  rise  of  70  degrees, 
let  us  take  the  first  case  given  in  Table  V.  Here 
.93  square  inch  of  steel  per  square  foot  section  of 
concrete  is  given;  67  per  cent  of  this  is  .62  square 
inch.  Hence  this  case  is  on  the  safe  side,  and  it 
is  easy  to  see  that  all  other  cases  are  still  safer. 


154      HANDBOOK    ON    REINFORCED    CONCRETE. 


Accordingly,  the  distribution  of  steel  here  given 
is  ample  to  care  for  the  tension  caused  by  both 
the  loading  and  the  expansion  in  one  direction 
produced  by  a  rise  of  70  degrees  F.  To  care  for 
the  tension  caused  by  a  like  expansion  in  the 
opposite  direction,  the  following  table,  giving  the 
sections  of  steel  to  resist  different  temperature 
changes,  is  inserted. 

TABLE  V«. 

Steel  Required  for  the  Following   Temperature  Changes 
(Placed  Parallel  with  the  Beams'). 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

(30°  F.) 

(40°  F.) 

(50°  F.) 

(60°  F.) 

(70°  F.) 

«« 

Z 

M 

1 

? 

— 

o 

rd     S 

—    fl)       • 

^  S  ^; 

_£H    3 

^c-t   gj     • 

w 

^     C     O 

v 

O   C   O 

%. 

«  C  0 

V 

w.s  ^ 

v 

v 

8u- 

S^     O 

cq 

w 

.ga  o 

cq 

C<l 

01 

0  o 

*£    jjj^ 

'"'  u 

*®  0><2 

1-1  CJ 

*  fcS 

In  W' 

'«  <Dq3 

1-1  o 

v  D 

"w  " 

i" 

Fl 

I6 

pi 

1' 

||| 

& 

|a"° 

1°' 

ill 

ld 

J  s"~ 

1^ 

g^ 

m  !  .2 

J|£ 

In. 

3.5 

.075 

fa 

.10 

1 

.125 

1 

.15 

A 

.175 

ft 

4 

.086 

ft 

.115 

I 

.143 

1 

.171 

7 

.20 

4.5 

.097 

ft 

.129 

1 

.161 

ft 

.193 

ft 

.225 

\ 

5 

.107 

f 

.143 

t 

.179 

ft 

.214 

i 

.25 

\ 

5.5 

.118 

t 

.157 

ft 

.197 

| 

.235 

\ 

.275 

ft 

6 

.129 

1  . 

.172 

^ 

.214 

£ 

.257 

\ 

.30 

I9. 

6.5 

.139 

f 

.186 

ft 

.232 

£ 

.279 

ft 

.325 

f 

7 

.15 

ft 

.20 

.25 

\ 

.30 

ft 

.35 

f 

7.5 

.161 

ft 

.214 

\ 

.268 

ft 

.321 

f 

.375 

f 

8 

.172 

ft 

.229 

\ 

.286 

A 

.343 

i 

.40 

ft 

8.5 

.183 

ft 

.243 

\ 

.304 

A 

.364 

f 

.425 

ft 

9 

.193 

.257 

ft 

.322 

1 

.386 

f 

.45 

ft 

9.5 

.204 

i 

.272 

ft 

.340 

f 

.407 

ft 

.475 

ft 

10. 

.215 

i 

.286 

A 

.358 

1 

.428 

ft 

.50 

f 

10.5 

.226 

i 

.300 

ft 

.376 

f 

.45 

ft 

.525 

f 

11 

.236 

i 

.314 

ft 

.394 

f 

.471 

ft 

.55 

f 

11.5 

.247 

.329 

f 

.412 

H 

.492 

t 

.575 

ft 

12 

.257 

* 

,344 

f 

.428 

H 

.514 

t 

.60 

If 

DESIGNS  OF  CONCRETE  STRUCTURES.    155 

DESCRIPTION  OF  TABLE  VI. 

This  table  serves,  in  the  design  of  floors,  as  does 
Table  II  in  the  design  of  beams  and  girders. 
When  the  span,  given  in  column  2,  and  the  net 
loading  per  square  foot  given  under  column  4,  are 
known,  the  corresponding  thickness  of  floor  may 
be  obtained  from  column  1.  By  the  net  loading 
per  square  foot  is  meant  the  live  loading.  Column 
3  gives  the  gross  loading  per  square  foot  which 
includes  both  the  live  and  the  dead  loading  due 
to  the  weight  of  the  floor  itself. 

Column  5  gives  the  deflection  in  inches  due  to 
the  gross  loading  and  the  span.  By  referring  to  a 
series  of  tests  upon  the  deflection  of  floors,  found 
in  Part  II,  it  will  be  observed  that,  while  the 
modulus  of  elasticity  of  the  girders  averaged  about 
3,000,000,  that  of  the  floors  at  the  center  of  the 
span,  averaged  only  about  1,600,000.  With  this 
in  view,  column  5  was  figured,  calling  the  modulus 
of  elasticity  1,500,000,  which  is  on  the  safe  side. 

Under  column  6  is  given  the  amount  of  ^-J^  of 
the  span  in  inches,  with  which  the  deflection 
under  column  5  may  be  compared.  Under  the 
description  of  Table  IV,  reasons  were  given  why  a 
deflection  of  -g^  of  the  span  is  allowable  in  the 
case  of  beams  or  girders.  Considering  this,  and 
in  cases  where  a  very  level  floor  is  desired,  the 
writer  has  underscored  the  longest  span  for  each 
size,  giving  a  deflection  within  the  limit.  In  cases 
where  a  strictly  level  floor  is  not  absolutely  neces- 


156        HANDBOOK   ON    REINFORCED    CONCRETE. 

sary,  the  limit  of  ¥J7  of  the  span  may  be  exceeded, 
and  surely,  by  the  excess  in  deflection  for  all  the 
spans  here  figured,  for  the  reason  that,  in  figuring 
the  deflection  under  column  5,  the  modulus  of 
elasticity  was  fixed  at  but  half  the  value  assigned 
to  it  when  a  deflection  of  -g-J-^  of  the  span  began 
to  cause  cracks.  Accordingly,  we  should  not 
expect  cracks  to  appear  until  the  deflection 
approached  the  value  ¥^7  of  the  span,  which 
is  borne  out  by  the  tests  just  referred  to  in 
Part  II. 

It  will  doubtless  appear  that  for  a  given  thick- 
ness of  floor,  and  with  the  ordinary  live  loads  met 
with  in  practice,  that  the  limiting  span  here  given 
is  very  small.  This  is  so,  first,  because  in  the 
design  here  given,  no  attempt  has  been  made  to 
help  out  the  moment  of  resistance  of  the  concrete 
in  compression  by  reinforcement.  On  the  other 
hand,  this  has  been  taken  as  a  basis  of  strength, 
and  enough  steel  has  been  inserted  to  make  the 
tensile  moment  of  resistance  equal  to  it.  By  in- 
serting steel  members  into  the  compression  side 
of  the  neutral  axis  and  at  the  same  time  into  the 
tension  side  to  balance  up,  the  same  thickness  of 
floor  may  be  designed  for  much  longer  spans,  but 
this  comes  under  special  designs,  which  are  not  to 
be  considered  here.  The  limit  of  this  reinforce- 
ment to  increase  the  moments  of  resistance  of 
compression  and  of  tension,  is  fixed  by  the  tensile 
stress  per  square  inch  coming  upon  the  layer  of 
concrete  between  the  steel  members  in  the  tensile 


DESIGNS    OF    CONCRETE    STRUCTURES. 


157 


layer,  which  must  be  kept  under  1,500  pounds,  as 
explained  in  the  description  of  Table  I.  The  sec- 
ond reason  is,  as  stated  in  the  description  of  Table 
V,  that  2  inches  is  added  to  the  thickness  of  the 
floor  from  which  no  benefit  as  regards  strength  is 
figured. 

TABLE  VI.  —  Floors. 


1 

2 

3 

4 

5 

6 

Span. 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

3.5 

2.5 

240 

196 

.032 

.038 

3.0 

167 

123 

.046 

.045 

3.5 

123 

79 

.063 

.053 

4.0 

94 

50 

.083 

.060 

4.5 

74 

30 

.104 

.068 

4.0 

2.5 

425 

375 

.024 

.038 

3.0 

296 

246 

.035 

.045 

3.5 

218 

168 

.048 

.053 

4.0 

167 

117 

.063 

.060 

4.5 

131 

81 

.079 

.068 

5.0 

106 

56 

.098 

.075 

5.5 

89 

39 

.115 

.082 

4.5 

2.5 

792 

735 

.024 

.038 

3.0 

459 

401 

.029 

.045 

3.5 

338 

281 

.040 

.053 

4.0 

258 

201 

.052 

.060 

4.5 

205 

148 

.066 

.068 

5.0 

165 

108 

.081 

.O7.r, 

5.5 
A  n 

137 

lit; 

80 
«n 

.099 

1  1  C 

t 

158      HANDBOOK   ON    REINFORCED    CONCRETE. 


TABLE  VI.  —  Floors.  —  Continued. 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

STilT 
Span. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

5.0 

2.5 

960 

896 

.017 

.038 

3.0 

667 

904 

.025 

.045 

3.5 

492 

429 

.032 

.053 

4.0 

375 

308 

.044 

.060 

4.5 

288 

224 

.055 

.008 

5.0 

240 

177 

.069 

.075 

5.5 

198 

134 

.084 

.082 

6.0 

167 

104 

.101 

.090 

6.5 

141 

78 

.117 

.098 

7.0 

122 

59 

.136 

.105 

5.5 

2.5 

1330 

1261 

.015 

.038 

3.0 

923 

854 

.022 

.045 

3.5 

680 

611 

.029 

.053 

4.0 

519 

450 

.038 

.060 

4.5 

411 

342 

.049 

.068 

5.0 

332 

263 

.060 

.075 

5.5 

275 

206 

.072 

.082 

6.0 

231 

162 

.086 

.090 

6  5 

197 

128 

.101 

.098 

7.0 

169 

100 

.117 

.105 

7.5 

148 

79 

.135 

.113 

8.0 

130 

61 

.154 

.120 

8.5 

115 

46 

.174 

.127 

9.0 

102 

31 

.193 

.135 

6.0 

3.0 

1185 

1110 

.019 

.045 

3.5 

873 

798 

.026 

.053 

4.0 

667 

592 

.038 

.060 

4.5 

528 

453 

.047 

.068 

5.0 

427 

252 

.052 

.075 

5.5    , 

354 

279 

.063 

.082 

6.0 

293 

218 

.074 

.090 

6.5 

253 

178 

.088 

.098 

DESIGNS    OF   CONCRETE   STRUCTURES. 


159 


TABLE  VI.  —  Floors.  —  Continued. 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

8  tj(7 

Span. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

6.0 

7.0 

218 

133 

.102 

.105 

7.5 

190 

115 

.117 

.112 

8.0 

167 

92 

.133 

.120 

8.5 

148 

73 

.149 

.127 

9.0 

132 

57 

.169 

.135 

9.5 

118 

43 

.188 

.144 

10.0 

107 

32 

.209 

.150 

6.5 

3.5 

1105 

1024 

.023 

.053 

4.0 

845 

764 

.030 

.060 

4.5 

669 

588 

.038 

.068 

5.0 

540 

460 

.046 

.075 

5.5 

449 

368 

.056 

.082 

6.0 

376 

297 

.067 

.090 

6.5 

322 

241 

.079 

.098 

7.0 

275 

194 

.090 

.105 

7.5 

241 

160 

.105 

.113 

8.0 

211 

130 

.118 

.120 

8.5 

188 

107 

.135 

.127 

9.0 

166 

85 

.150 

.135 

9.5 

150 

69 

.168 

.143 

10.0 

135 

59 

.186 

.150 

10.5 

123 

42 

.205 

.158 

11.0 

112 

31 

.225 

.165 

7.0 

4.0 

1042 

955 

.027 

.060 

4.5 

824 

937 

.034 

.068 

5.0 

674 

587 

.043 

.075 

5.5 

553 

466 

.051 

.082 

6.0 

463 

376 

.061 

.090 

6.5 

395 

308 

.071 

.098 

7.0 

341 

254 

.083 

.105 

7.5 

297 

210 

.096 

.113 

8.0 

260 

173 

.108 

.120 

160       HANDBOOK   ON   REINFORCED   CONCRETE. 


TABLE  VI.  —  Floors.  —  Continued. 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

t$u 

Span. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches, 

Inches. 

7.0 

8.5 

231 

144 

.122 

.128 

9.0 

207 
186 

120 
99 

.138 
.155 

.135 
.143 

95 

10.0 

166 

79' 

.168 

.150 

10.5 

151 

64 

.186 

.158 

11.0 

138 

51 

.204 

165 

11.5 

126 

39 

.223 

.173 

12.0 

116 

29 

.243 

.180 

7.5 

4.0 

1260 

1166 

.025 

.060 

4.5 

996 

902 

.031 

.068 

5.0 

806 

712 

.044 

.075 

5.5 

667 

573 

.047 

.082 

6.0 

560 

466 

.056 

.090 

. 

6.5 

478 

384 

.066 

.098 

7.0 

411 

317 

.076 

.105 

7.5 

359 

265 

.087 

.113 

8.0 

315 

221 

.100 

.120 

8.5 

280 

186 

.113 

.128 

9.0 

250 

156 

.127 

.135 

9.5 

224 
202 

130 
108 

.142 
.156 

.143 
.150 

10.0 

10.5 

193 

99 

.171 

.158 

11.0 

167 

73 

.189 

.165 

11.5 

153 

59 

.206 

.173 

12.0 

140 

46 

.224 

.180 

12.5 

129 

35 

.243 

.198 

8.0 

4.5 

1186 

1087 

.029 

.068 

5.0 

960 

860 

.036 

.075 

5.5 

797 

697 

.043 

.083 

6.0 

667 

567 

.052 

.090 

6.5 

570 

470 

.061 

.098 

7.0 

490 

390 

.070 

.105 

DESIGNS   OF   CONCRETE   STRUCTURES. 
TABLE  VI.  —  Floors.  —  Continued. 


161 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

8"57 

Span. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

8.0 

7.5 

427 

327 

.080 

.113 

8.0 

375 

275 

.092 

.120 

8.5 

334 

234 

.104 

.128 

9.0 

296 

196 

.116 

.135 

9.5 

267 

167 

.130 

.143 

10.0 

240 

140 

.144 

.150 

10.5 

218 

118 

.158 

.158 

11.0 

198 

98 

.174 

.165 

11.5 

182 

82 

.190 

.173 

12.0 

167 

67 

.206 

.180 

12.5 

154 

54 

.225 

.188 

13.0 

142 

42 

.242 

.195 

13.5 

131 

31 

.260 

.203 

8.5 

5.0 

1126 

1020 

.033 

.075 

5.5 

933 

827 

.040 

.083 

6.0 

783 

677 

.048 

.090 

6.5 

667 

561 

.056 

.098 

7.0 

575 

469 

.065 

.105 

7.5 

502 

396 

.075 

.113 

8.0 

440 

334 

.085 

.120 

8.5 

391 

285 

.097 

.128 

9.0 

348 

242 

.108 

.135 

9.5 

313 

207 

.120 

.143 

10.0 

282 

176 

.133 

.150 

10.5 

255 
233 

149 
127 

.146 
.161 

.158 
.165 

11.0 

11.5 

212 

106 

.175 

.173 

12.0 

195 

89 

.191 

.180 

12.5 

181 

75 

.209 

.188 

13.0 

167 

61 

.226 

.195 

13.5 

155 

49 

.243 

.203 

14.0 

144 

38 

.262 

.210 

162       HANDBOOK   ON    REINFORCED    CONCRETE. 


TABLE  VI.  —  Floors.  —  Continued. 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
grot*.. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

»o~s 
Span. 

Inches. 

Feet. 

Lbs, 

Lbs. 

Inches, 

Inches. 

9.0 

6.0 

906 

793 

.045 

.090 

6.5 

773 

660 

.053 

.098 

7.0 

666 

553 

.061 

.105 

7.5 

582 

469 

.070 

.113 

8.0 

510 

397 

.080 

.120 

8.5 

454 

341 

.091 

.128 

9.0 

404 

291 

.101 

.135 

9.5 

362 

249 

.112 

.143 

10.0 

326 

213 

.124 

.150 

10.5 

296 

183 

.137 

.158 

11.0 

270 

157 

.150 

.165 

11.5 

248 

135 

.165 

.173 

12.0 

227 
209 

114 
96 

.179 
.195 

.180 
.188 

12.5 

13.0 

193 

80 

.210 

.195 

13.5 

179 

66 

.226 

.203 

14.0 

162 

49 

.237 

.210 

9.5 

6.5 

890 

771 

.049 

.098 

7.0 

766 

647 

.057 

.105 

7.5 

670 

553 

.066 

.113 

8.0 

586 

467 

.074 

.120 

8.5 

521 

402 

.084 

.128 

9.0 

463 

342 

.094 

.135 

9.5 

417 

298 

.105 

.143 

10.0 

375 

256 

.116 

.150 

10.5 

341 

222 

.128 

.158 

11.0 

310 

191 

.140 

.165 

11.5 

284 

165 

.154 

.173 

12.0 

261 

142 

.168 

.180 

12.5 

240 
222 

121 
103 

.182 
.197 

.188 
.195 

13.0 

13.5 

207 

88 

.213 

.203 

14.0 

192 

73 

.228 

.210 

14.5 

179 

60 

.245 

.218 

15.0 

165 

46 

.259 

.225 

DESIGNS   OF   CONCRETE    STRUCTURES. 


163 


TABLE  VI.  —  Floors.  —  Continued. 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

m 
Span. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

10.0 

7.0 

870 

745 

.053 

.105 

7.5 

760 

635 

.061 

.113 

8.0 

669 

534 

.070 

.120 

8.5 

592 

467 

.079 

.128 

9.0 

527 

402 

.089 

.135 

9.5 

473 

348 

.099 

.143 

10.0 

426 

301 

.109 

.150 

10.5 

388 

263 

.121 

.158 

11.0 

353 

228 

.132 

.165 

11.5 

323 

198 

.144 

.173 

12.0 

296 

171 

.156 

.180 

12.5 

273 

148 

.170 

.188 

13.0 

252 

127 

.189 

.195 

13.5 

235 

110 

.200 

.202 

14.0 

218 

93 

.215 

.210 

14.5 

204 

79 

.231 

.218 

15.0 

190 

65 

.246 

.225 

15.5 

178 

53 

.263 

.233 

10.5 

7.5 

857 

726 

.058 

.113 

8.0 

753 

622 

.066 

.120 

8.5 

670 

539 

.075 

.128 

9.0 

595 

432 

.084 

.135 

9.5 

534 

403 

.094 

.143 

10.0 

482 

351 

.104 

.150 

10.5 

438 

307 

.115 

.158 

11.0 

398 

267 

.125 

.165 

11.5 

364 

233 

.136 

.173 

12.0 

335 

204 

.149 

.180 

12.5 

309 

178 

.162 

.188 

13.0 

285 

154 

.175 

.195 

13.5 

264 

133 

.188 

.203 

14.0 

246 

115 

.203 

.210 

14.5 

229 

98 

.218 

.218 

15.0 

215 

84 

.234 

.225 

164       HANDBOOK   ON   REINFORCED   CONCRETE. 


TABLE  VI.  —  Floors.  —  Continued. 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

Span. 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

10.5 

15.5 

201 

70 

.249 

.233 

16.0 

188 

57 

.264 

.240 

11.0 

8.0 

780 

642 

.058 

.120 

8.5 

692 

554 

.066 

.128 

9.0 

618 

480 

.074 

.135 

9.5 

555 

417 

.083 

.143 

10.0 

500 

362 

.091 

.150 

10.5 

453 

315 

.101 

.158 

11.0 

415 

277 

.111 

.165 

11.5 

378 

240 

.121 

.173 

12.0 

348 

210 

.132 

.180 

12.5 

320 

182 

.143 

.188 

13.0 

295 

157 

.154 

.195 

13.5 

275 

137 

.167 

.203 

14.0 

255 

117 

.179 

.210 

14.5 

238 

100 

.193 

.218 

15.0 

223 

85 

.207 

.225 

15.5 

208 
196 

70 

58 

.220 
.234 

.233 
.240 

16.0 

16.5 

184 

46 

.249 

.248 

11.5 

7.0 

1233 

1089 

.046 

.105 

7.5 

1085 

940 

.054 

.113 

8.0 

940 

795 

.060 

.120 

8.5 

838 

693 

.068 

.128 

9.0 

746 

602 

.076 

.135 

9.5 

670 

526 

.085 

.143 

10.0 

604 

459 

.094 

.150 

10.5 

549 

405 

.104 

.158 

11.0 

500 

356 

.114 

.165 

11.5 

458 

314 

.125 

.173 

12.0 

420 

276 

.135 

.180 

12.5 

387 

240 

148 

.188 

13.0 

357 

213 

.159 

.195 

DESIGNS    OF   CONCRETE    STRUCTURES. 
TABLE  VI.  —  Floors.  —  Continued. 


165 


1 

2 

3 

4 

5 

6 

Thickness 
of 
floor. 

Span. 

Load 
square  foot, 
gross. 

Load 
square  foot 
net. 

Deflection 
caused  by 
loading. 

"SITU 
Span 

Inches. 

Feet. 

Lbs. 

Lbs. 

Inches. 

Inches. 

11.5 

13.5 

322 

188 

.167 

.203 

14.0 

309 

165 

.185 

.210 

14.5 

288 

144 

.198 

.218 

15.0 

268 

124 

.212 

.225 

15.5 

251 

107 

.226 

.233 

16.0 

236 

91 

.241 

.240 

16.5 

222 

78 

.257 

.248 

17.0 

210 

66 

.273 

.255 

17.5 

197 

53 

.288 

.263 

12.0 

7.5 

1186 

1036 

.049 

.113 

8.0 

1042 

892 

.057 

.120 

8.5 

925 

775 

.064 

.128 

9.0 

823 

673 

.072 

.135 

9.5 

740 

589 

.080 

.143 

10.0 

666 

516 

.088 

.150 

10.5 

604 

454 

.097 

.158 

11.0 

552 

402 

.107 

.165 

11.5 

504 

354 

.116 

.173 

12.0 

463 

313 

.127 

.180 

12.5 

427 

279 

.138 

.188 

13  0 

395 

245 

.150 

.195 

13.5 

366 

216 

.161 

.203 

14.0 

340 

190 

.173 

.210 

14.5 

318 

168 

.180 

.218 

15.0 

304 

154 

.204 

.225 

15.5 

278 

128 

.212 

.233 

16.0 

260 

110 

.225 

.240     . 

16.5 

245 

95 

.240 

.248 

17.0 

230 

80 

.254 

.255 

17.5 

218 

68 

.270 

.263 

18.0 

206 

56 

.286 

.270 

166      HANDBOOK   ON   REINFORCED   CONCRETE. 

DESCRIPTION  OF  TABLE  VII. 

This  table  gives,  for  different  sizes  of  columns, 
both  with  circular  and  with  octagonal  sections, 
the  corresponding  safe  total  load  in  tons  that  the 
same  will  carry,  paying  due  regard  to  the  ratio  of 
height  to  diameter  by  caring  for  eccentricity  of 
loading.  In  determining  the  sizes,  the  concrete 
alone  was  figured  to  withstand  by  compression  the 
total  loading,  while  the  steel  inserted  within  the 
concrete,  was  designed  to  resist  all  stress  both  of 
tension  and  of  compression  caused  by  bending, 
due  to  any  eccentricity  of  loading  as  stated  be- 
low. The  portion  of  load,  limiting  the  amount  of 
eccentricity,  was  fixed  at  one  quarter  of  the  total 
loading,  and  the  amount  cared  for  was  that  due 
to  this  loading  acting  about  a  leverage  of  an 
amount  equal  to  the  effective  radius  of  the  column. 
By  the  effective  radius  is  meant  the  distance  from 
the  center  of  the  column  to  the  center  of  the  steel 
bars. 

Circular  and  octagonal  shapes  were  figured  be- 
cause they  allow  for  the  most  effective  arrange- 
ment of  the  rods,  and  besides,  octagonal  shapes 
are  very  successfully  formed.  It  is  also  designed 
to  use  eight  rods  in  each  case,  spaced  equally 
apart  around  the  column,  and  at  a  distance  from 
the  center  of  the  column  equal  to  1  inch  less  than 
the  radius.  Eight  rods  thus  placed  give  the  great- 
est moment  of  resistance  about  any  axis  for  a 
given  amount  of  material,  and  hence  are  the  most 
economical. 


DESIGNS    OF   CONCRETE    STRUCTURES. 
TABLE  VII.  —  Columns. 


167 


Circular  section. 

Octagonal  section. 

1 

Size 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Area 
section. 

Weight 
per 
foot. 

Safe 
load. 

Height 
of 
col- 
umn. 

Size 
of 
rods. 
(Use  8.) 

Weight 
foot. 

Safe 
load. 

Height 
of 
col- 
umn. 

Size 
of 
rods. 

In. 

Sq.  in. 

Lbs. 

Tons. 

Feet. 

In. 

Lbs. 

Tons. 

Feet. 

In. 

5 

19.6 

20 

8.3 

4-6 

A 

18 

7.5 

4-6 

A 

7-11 

i 

7-11 

i 

12 

& 

12 

A" 

6 

28.0 

?9 

11.9 

5 

A 

26 

10.3 

5-6 

A 

6-9 

i 

7-10 

i 

10-15 

A 

11-15 

A 

7 

38.5 

40 

16.4 

6-7 

i 

36 

14.8 

6-8 

i 

8-12 

TS 

9-13 

A 

13-17 

1 

14-17 

f 

8 

50.3 

52 

21.4 

7-10 

A 

47 

19.3 

7 

I 

11-15 

f 

8-12 

A 

16-20 

A 

13-17 

1 

18-20 

T6 

9 

63.6 

66 

27 

8-9 

A 

60 

24.4 

8-10 

A 

10-13 

1 

11-15 

1 

14-19 

A 

16-20 

T6 

20 

i 

10 

78.5 

82 

33.4 

9-12 

1 

74 

30.0 

9 

A 

13-17 

TJ> 

10-14 

f 

18-20 

| 

15-19 

A 

20 

i 

11 

95.0 

99 

40.4 

8-11 

i 

89 

36.5 

8 

A 

12-15 

10-12 

f 

16-20 

| 

13-17 

A 

18-20 

i 

12 

113.0 

118 

48.0 

8-10 

1 

106 

43.3 

8-11 

f 

11-14 

T5 

12-15 

A 

15-18 

| 

16-20 

^ 

19-20 

A 

168 


HANDBOOK    ON  REINFORCED    CONCRETE. 


TABLE  VII.  —  Columns.  —  Continued. 


Circular  section. 

Octagonal  section. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Height 
of 
col- 
umn. 

10 

Size 
of 
rods. 

Size. 

Area 
section. 

Weight 
per 
foot. 

Safe 
load. 

Height 
of 
col- 
umn. 

Size 
of 
rods. 

(Use  8.) 

Weight 
foot. 

Safe 
load. 

In. 

Sq.  in. 

Lbs. 

Tons. 

Feet. 

In. 

Lbs. 

Tons. 

Feet. 

In. 

13 

132.7 

138 

56.5 

8-9 

1 

125 

51.0 

8-10 

|^ 

10-13 

7 
T6 

11-14 

TS 

14-17 

J 

15-19 

| 

18-20 

T5 

20 

A 

14 

153.9 

160 

65.5 

8-9 

f 

144 

59.0 

8-10 

| 

10-12 

11-13 

T5 

13-16 

f 

14-18 

I 

17-20 

TS 

19-20 

A 

15o 

176.7 

184 

75.2 

8-11 

ft 

166 

67.8 

8 

f 

12-15 

| 

9-12 

16-18 

A 

13-16 

* 

19-20 

1 

17-20 

A 

16 

201.0 

210 

85.5 

8-10 

ft 

189 

77.0 

8 

f 

11-14 

£ 

9-11 

ft 

15-17 

A 

12-15 

i 

18-20 

f    • 

16-19 

A 

20 

f 

17 

227.0 

236 

96.5 

8-10 

A 

213 

87.0 

8 

| 

11-13 

1 

9-11 

ft 

14-16 

A 

12-14 

i 

17-20 

f 

15-18 

ft 

19-20 

f 

18 

254.5 

255 

108.0 

8-9 

A 

239 

97.5 

8-10 

ft 

10-12 

i 

11-13 

1 

13-15 

A 

14-17 

A 

16-19 

f 

18-20 

f 

20 

T! 

19 

283.5 

295 

120.5 

8-9 

ft 

266 

109.0 

8-9 

ft 

10-11 

1 

10-13 

i 

12-14 

A 

14-16 

A 

15-18 

f 

17-20 

f 

19-20 

tt 

DESIGNS  OF  CONCRETE  STRUCTURES. 


169 


TABLE  VII.  —  Columns.  —  Continued. 


Circular  section. 

Octagonal  section. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Size. 

Area 
section. 

Weight 
per 
foot. 

Safe 
load. 

Height 
of 
col- 
umn. 

Size 
of 
rods. 

(Use  8). 

Weight 
per 
foot. 

Safe 
load. 

Height 
of 
col- 
umn. 

Size 
of 
rods. 

In. 

Sq.  in. 

Lbs. 

Tons. 

Feet. 

In. 

Lbs. 

Tons. 

Feet. 

In. 

20 

314.1 

327 

133.3 

8 

7 

295 

120.0 

8-9 

A 

9-11 

1 

10-12 

i 

12-14 

13-15 

A 

15-17 

1 

16-19 

f 

18-20 

ft 

20 

ft 

22 

380 

396 

161.7 

8-10 

1 

S58 

145.0 

8 

TS 

11-12 

A 

9-11 

% 

13-15 

f 

12-14 

A 

16-19 

ft 

15-17 

f 

20 

f 

18-20 

ii 

24 

452 

472 

192.4 

8-9 

i 

427 

173.5 

8-10 

i 

10-11 

A 

11-12 

A 

12-14 

f 

13-15 

I 

15-17 

ft 

16-19 

18-20 

1 

20 

I 

26 

531 

553 

225.5 

8 

^ 

500 

203.2 

8-9 

1 

9-10 

& 

10-11 

A 

11-12 

f 

12-14 

f 

13-16 

ft 

15-18 

ft 

17-19 

f 

19-20 

t 

20 

tt 

28 

616 

641 

262.0 

8 

) 

578 

235.0 

8 

i 

9 

TS 

9-11 

A 

10-12 

f 

12-13 

f 

13-15 

ft 

14-16 

ft 

16-18 

f 

17-20 

t 

19-20 

ft 

30 

707 

735 

300.0 

8-9 

TS 

662 

270.0 

8 

1 

10-11 

f 

9-12 

A 

12-14 

ft 

13-15 

f 

15-16 

f 

16-18 

ft 

17-19 

ft 

19-20 

t 

20 

1 

170      HANDBOOK   ON    REINFORCED   CONCRETE. 

DESCRIPTION  OF  TABLE  VIII. 

Table  VIII  is  drawn  up  both  to  facilitate  making 
estimates,  and  to  show  at  a  glance  the  compara- 
tive costs,  for  equal  strength,  of  the  three  kinds 
of  construction  given  —  namely,  reinforced  con- 
crete, structural  steel,  and  slow-burning,  when 
used  in  the  design  of  floors  in  the  shape  of  beams 
or  girders. 

The  basis  of  the  cost  of  the  concrete  given  under 
column  3  is  from  data  taken  by  the  writer  upon 
actual  work,  and  represents  fair  working  condi- 
tions. It  includes  all  temporary  false  work,  and 
everything  to  make  a  finished  piece  of  work,  and 
even  allows  going  over  the  exposed  surface  with  a 
cement  wash  after  pointing  up  and  removing 
irregularities  where  necessary.  The  cost  of  the 
steel  used  in  connection  with  the  concrete,  is  based 
upon  the  price  f.o.b  of  2  cents  per  pound,  to 
which  is  added  another  2  cents  per  pound  for 
handling,  cutting  to  lengths,  placing  in  forms,  and 
wiring  to  place  where  necessary. 

The  cost  of  the  structural  shapes  given  under 
column  7  is  based  upon  a  price  of  2.5  cents  per 
pound  f.o.b,  to  which  is  added  $10  per  ton,  or 
-J  cent  per  pound  to  cover  the  cost  of  placing, 
bolting,  or  riveting  to  place,  and  painting,  which 
is  little  enough. 

The  cost  of  wooden  beams  is  figured  upon  a 
basis  of  a  price  of  $35  per  thousand  feet  upon  the 
site  for  planed  stock,  which  is  increased  by  $10 


COMPARATIVE   COSTS.  171 

per  thousand  feet  to  cover  the  cost  of  sizing, 
placing,  and  fitting,  but  no  other  finish.  The  cost 
of  the  slow-burning  construction,  as  figured  here, 
applies  principally  to  northern  sections  of  the 
country,  and  should  be  considerably  reduced  to 
meet  southern  conditions. 


172       HANDBOOK    ON    REINFORCED    CONCRETE. 
I 


9 


&q 


slils'^00 


xxxxxxxxxxxxxx 


i 


00    W 
M    CO 


oo   10  o   o  <-*   I-H 

^H     (M     CO    CO    CO     CO 


CD     00    £- 

i 


oo-. 

O          ~ 


|XXXXXXXXXXXXXX 


si  I 
safe 


COMPARATIVE  COSTS. 


173 


x  x  x  x  x  x  x   :    ;    ;       ;       :  :   : 


xxxxxxxxxxxxxxxx 


174       HANDBOOK   ON   REINFORCED   CONCRETE. 

DESCRIPTION  OF  TABLE  IX. 

The  purpose  of  this  table  is  to  give  a  compara- 
tive cost,  for  equal  strength,  of  a  fire  resisting, 
reinforced  concrete  floor  in  comparison  with  the 
ordinary  floor  used  in  the  slow-burning  construc- 
tion. 

The  cost  of  the  concrete  given  under  column  3 
is  based  upon  actual  results  under  ordinary  con- 
ditions, but  differs  in  the  price  per  unit  of  volume 
from  that  of  beams  and  girders.  The  cost  of 
steel  given  under  column  4  is  figured  upon  the 
same  basis  as  was  explained  in  Table  VIII.  The 
item,  "Cost  of  Troweling,"  includes  the  cost  of 
labor  both  in  applying  the  1-inch  finish,  and  the 
screeding  and  troweling  same  to  a  finished  surface. 

For  wooden  floors,  the  price  here  given  is  based 
upon  the  cost  of  spruce  plank  laid  at  $35  per 
thousand  feet;  of  southern  pine  laid  at  $45;  of 
1-inch  No.  2  maple  top  flooring  laid  and  dressed 
at  $60;  and  No.  1  maple  at  $80  per  thousand 
feet. 


COMPARATIVE  COSTS. 


175 


TABLE  IX.  —  Comparative  Costs.  —  Floors  for  Equal 
Strength. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

Reinforced  concrete. 

Wood. 

Safe 

moment 

Cost 

Cost 

Cost 

inch-lbs. 

Thick- 
ness 

of 
con- 

Cost 
of 

of 
trowel- 

Total 
cost 

Spruce 
or 

Cost 
of 

per 
sq.  ft. 

Total 
cost 

Total 
cost 

p6r 
foot 
width. 

of 
floor. 

crete 
per 
sq.  ft. 

steel 
per 
sq.  ft. 

ing 
per 
sq.  ft. 

per 
sq.  ft. 

H.P. 

plank 
size. 

same 
per 
sq.  ft. 

maple 
No.  2 
top 

No.  2 
top 
floor. 

No.  1 
top 
floor. 

floor. 

In. 

Spruce 

2,250 

3.5 

$0.13 

$0.04 

$0.03 

$0.20 

2" 

$0.07 

$0.06 

$0.13 

$0.15 

4,000 

4.0 

.15 

.05 

.03 

.23 

2" 

.07 

.06 

.13 

.15 

6,200 

4.5 

.17 

.05 

.03 

.25 

2// 

.07 

.06 

.13 

.15 

9,000 

5.0 

.19 

.07 

.03 

.29 

3" 

.11 

.06 

.17 

.19 

12,450 

5.5 

.21 

.10 

.03 

.33 

3" 

.11 

.06 

.17 

.19 

16,000 

6.0 

.23 

.11 

.03 

.37 

4" 

.14 

.06 

.20 

.22 

20,250 

6.5 

.24 

.11 

.03 

.38 

4" 

.14 

.06 

.20 

.22 

25,000 

7.0 

.26 

.13 

.03 

.42 

4" 

.14 

.06 

.20 

.22 

* 

H.P. 

30,250 

7.5 

.28 

.13 

.03 

.44 

4" 

.18 

.06 

.24 

.26 

36,000 

8.0 

.30 

.13 

.03 

.46 

5" 

.23 

.06 

.29 

.31 

42,250 

8.5 

.32 

.15 

.03 

.50 

5" 

.23 

.06 

.29 

.31 

49,000 

9.0 

.34 

.15 

.03 

.52 

5" 

.23 

.06 

.29 

.31 

56,250 

9.5 

.36 

.18 

.03 

.57 

6" 

.27 

.06 

.33 

.35 

64,000 

10.0 

.38 

.18 

.03 

.59 

6" 

.27 

.06 

.33 

.35 

72,250 

10.5 

.39 

.18 

.03 

.60 

6" 

.27 

.06 

.33 

.35 

176      HANDBOOK   ON    REINFORCED    CONCRETE. 


DESCRIPTION  OF  TABLE  X. 

Table  X  is  similar  in  all  respects  to  Table  IX, 
but  compares  the  two  kinds  of  constructions  upon 
a  fairer  basis  —  that  is,  the  relative  costs  for 
like  stiffness  or  for  like  deflections.  Since  rein- 
forced concrete,  because  of  a  high  modulus  of 
elasticity,  gives  a  stiffer  floor  than  does  the  wood, 
this  basis  of  comparison  as  regards  cost,  more 
nearly  shows  up  the  concrete  floor  in  its  proper 
merits  in  this  particular  sphere. 


TABLE  X.  —  Comparative  Costs.  —  Floors  for  Equal 
Deflection. 


1 

2 

3 

4 

5 

6 

7 

Reinforced  concrete. 

Wood. 

Safe 

moment 
in  inch- 
pounds 
per  foot 
width. 

Thickness 
of 
floor. 

Actual 

resist- 
ing 
depth. 

Cost 
per 
sq.   ft. 
com- 
plete. 

Thickness 
of  spruce 
or  H.  P. 
plank. 
(Inches.) 

Total  cost 
per  sq.  ft. 
with  No.  2 
maple  top 
floor. 

Total  cost 
per  sq.  ft. 
with  No.  1 
maple  top 
floor. 

Inches. 

Inches. 

Spruce. 

2,250 

3.5 

1.5 

$0.20 

2" 

$0.13 

$0.17 

4,000 

4.0 

2.0 

.23 

3" 

.17 

.19 

6,200 

4.5 

2.5 

.25 

4" 

.20 

.22 

H.  P. 

9,000 

5.0 

3.0 

.29 

4" 

.24 

.26 

12,400 

5.5 

3.5 

.33 

5" 

.29 

.31 

16,000 

6.0 

4.0 

.37 

5" 

.29 

.31 

20,250 

6.5 

4.5 

.38 

6" 

.33 

.35 

COMPARATIVE   COSTS.  177 

DESCRIPTION  OF  TABLE  XI. 

The  following  table  is  given  both  to  assist  in 
estimating  the  cost  of  reinforced  concrete  columns, 
and  to  serve  as  a  means  of  comparison  in  cost 
between  the  more  general  forms  of  construction  — 
namely,  cast  iron,  steel  or  wrought  iron,  and 
wood. 

As  before,  the  cost  given  here  for  reinforced 
concrete  is  taken  from  average  results  of  actual 
construction  of  columns.  The  basis  of  computing 
the  cost  of  the  other  kinds  of  columns  is  taken: 
for  cast  iron,  2.5  cents  per  pound,  erected  in  the 
building;  for  steel,  3  cents  per  pound  for  plain 
shapes,  and  3.5  cents  for  riveted  sections  erected; 
and  for  wood  $45  per  thousand  feet  in  place. 


178      HANDBOOK   ON   REINFORCED   CONCRETE. 


1 

iH 

6ll 

S22      228      228 

'i        'i 

I-H    CO    U5 

i   r 

00    00 

1-H      CO 

•H 

HI 

1                         ?              7 

•    g  TP  »o  r>.        »o»oco        cocoi> 

1—  I 

CO    b-    0 

1 

O 

1-i 

$ 

II   i;..v    M? 

i- 

i 

0> 

ii 

.d         -co          -oo               -co 

J.J,              •     CO                              Tji                         -CO 

•     •  06 

00 

ill 

'  2 

s 

&J 

:  ** 

"I 

^  .S    7 

J. 

:  «H. 

d 

o  g'S     S 

:  :  ;    :  :  ;    :  ;  : 

•  x 

l1lxl 

d       ;           ;       .'       ;    ;    ; 

^    -*> 

3~sJ-S  S 

(NiOOO           COO5<N            COCOIN 

-H     t-     <N 

(0 

lllll 

i 

1 

10 

I1!!! 

i 

2  2  S 

S 

3 
I 

, 

ill 

§              S              2 
g 

a 

'S 

5     d 

.          ^                                    ^                     ^    ^ 

2  12  3 

o 

d 

CO 

w°l 

*2lJ-cN            ROCOCO            COOOCO 

^! 

0 

<N 

P     « 

,a  io                   co                   t^ 
o 

c 

00 

«H 

,2  73 
03  c8 
02^ 

g  CO                              O5                              •* 
O  oo                            I-H                            CO 

si 

COMPARATIVE    COSTS.  179 

<N    •*    lO            <N    CC    iO            00    CO    »O  CO    CO    ••*    »O  ^    "*    **    *°.  * 

i  £         &$         & 

1-1  o  w  cxi  '. 

I>0><N            OOOS^H            0>050  O    O    i-H    <N  ^H^H^IM  : 

!  I   JS  j  :   j      S  : 

i-l                             •     i-H                   •               ^H  •     (N         •  (N 

00                     •    TJJ                         (N  •    <N       •'  (O 

O                     -CO                          to  •       •    Oi       •  •       •           (N  • 

i  .      .   «*      .  •       •           (M 

OOO            OOOOO            OOOOO  OOOOIO1O  OINlOO  (NiO 

XX    XX  »X    XXX  XXXX  XXXX  XX 

COOO            «OI>00            tOI>00  t^OOOOOO  I>OOOOOS  0000 


OOO'tO  OSCOOO  00(NCO  OOrHiqp  OOO 


?  7 

oo  o 


8  3 


180      HANDBOOK   ON   REINFORCED  CONCRETE. 


£  . 

!  «5          !          !  »o          .          .  o 

| 

S 

^si 

:  g       :                   :        : 

0 

3 

•Si 

o     '•   d            •               N            •            -co 

££o 

fl        .     ,-1                   .                         rH                   •                   -r-l 

1 

S 

ill 

:g        :          S        :        :§ 

o> 

1 

_fl      •    C<l                •               •    »-i                                •    N 

00 

ill 

gS           goo.g-          gSgg           g. 

O  ^'53 

(N<N            (M(N(N(N            (N(N<NCO            (NiN 

s 

it 

p 

& 

1 

1 

t* 

««  c-2     " 

^         HQO         HOOPH|OO         HOC         NoeH<»H<»'HN'                ^ 

^XX         XXXX         XXXX         XX 

§O5O           O5O5OO           O5OOO           O5O 

'-£ 

M8B  I 

o 

-g*O  Q 

1 

CO 

,-lts.               IO     <—  1     t>     CO               lCrHt>CO               lOi-l 
0505            C500-;            0    ^H    rH    (N            rH(N 

R 

H°S.|1 

0                                ^^^              ^^^rH              ^^ 

^ 

-^"-i 

n 
•* 

^^^  °i 

NW            ££«§            NNM^            C^c5 

H 

1 

i^lfl 

g 

i 

<s||oc- 

^                                                 TH                                                 ^ 

s 

<l 

•g  1^5  § 

'Td 

r9  O  fe'&Q 

o 

2 

^«a^8 

^ 

^  i 

^00           ^>0000           0«£0           OCO 

I 

« 

|S  S    SSS2    SISS    Jb  ^ 

s 

W    8 

0 

1    d 
«_,  3 

1 

W 

S  o  S 

O                                 rH                                             l^                                             i~* 

a 

<c   • 

TO                          o»                                    >C                                    U5 

*"* 

Si 

s        s           s           s 

COMPARATIVE    COSTS. 


181 


<N  CO     <N  (N  CO  CO  CO     <N  CO  CO  CO  CO 


-t~,    H«  HOC  »4*  -4*  Hhd 

XX    XXXXX    XXXXX    XXXXX    XXXXX 


COO  (NIOO5 


COO 

t-H<N  O)      i-H      iH      i-H  O      i-l      i-H      TH      C4 

•*l^  OOOCOCOO  OOO<N>OOJ  OOO5INICOO  OO'-HMcO 


HANDBOOK  ON  REINFORCED  CONCRETE. 


- 

t?  °£ 

Sj 

«9 

o 

. 

iH 

"883 

a  c«  S 
&  3  3 

1  :       :  :••:       if:      :;.: 

^0^ 

:       :    '  §       :   i    :       :  § 

| 

S 

6|I 

•     05                                 •                 •     0 

CO 

e> 

l| 

a    •'     '•     '•     '.               '.'.'. 

00 

iii 

OOiOQON-iC            OOKt^iOlOCN 

§ 

°^ 

8 

ia 

,  -i  ^ 

^r^^^HMHC,             C^r^r^HC,^^ 

0 

t- 

j||x| 

-CXXXXX         XXXXXX 

M8B  g 

(0 

&J5  o 

OOTt<COrHCN               OOTt*COi-ICMCO 
OrHfNCO-*            IOCOI>OOO5O 

<N    CN    <N    (N    CN           CM    (N    (N    <N    CN    CO 
€£ 

3-slli 

<NCOTJ<»OCO           <NCOrt<»C;Ot> 

I 

i*it! 

g 

"3 

o 

•<* 

00                                            CO 

rH                                                            (N 

oncrete  (ci 

eo 

w 

a    g 

^j             rHT(<t^O                         OtNCOO 
^OOOCMiCOO            OOO5rHCOI>O 

0 

" 

1     a 

hi 

g  1 

Jai              s 

rH 

II 

li         i 

COMPARATIVE   COSTS. 


183 


«s|oo  io|ao  e^x  «|ao         >o|oc  wlao  «NI  coMi  wh*  <o|ao 

xxxxxx   xxxxxx 


(NWINCOCCCO  CQCCOOCCCO 


<N    iO    00    O 

ooocoo        OOO<NIO 


184 


HANDBOOK   ON   REINFORCED    CONCRETE. 


TABLE  XI.  —  Continued. 
CONCRETE  —  OCTAGONAL  SECTION. 


1 

2 

3 

4 

5 

6 

Safe  load. 

Circum- 
scribed 
diameter 
of  column. 

Height  of 
column. 

Cost  of  con 
crete  per 
foot  heigh 
of  column. 

Cost  of 
steel  per 
foot  height 
of  column. 

Total  cost 
per  foot 
height  of 
column. 

Tons. 

Inches. 

Feet. 

7.5 

5 

4-6 

$0.07 

$0.04 

$0.11 

7-11 

.07 

.14 

12 

.10 

.17 

10.3 

6 

5-6 

.10 

.04 

.14 

7-10 

.07 

.17 

11-15 

.10 

.20 

14.8 

7 

6-8 

.14 

.07 

.21 

9-13 

.10 

.24 

14-17 

.16 

.30 

19.3 

8 

7 

.19 

.07 

.26 

8-12 

.10 

.29 

13-17 

.16 

.35 

18-20 

.21 

.40 

24.4 

9 

8-10 

.24 

.10 

.34 

11-15 

.16 

.40 

16-20 

.21 

.45 

30.0 

10 

9 

.30 

.10 

.40 

10-14 

.16 

.46 

15-19 

.21 

.51 

20 

.27 

.57 

36.5 

11 

8 

.36 

.10 

.46 

10-12 

.16 

.52 

13-17 

.21 

.57 

18-20 

.27 

.63 

43.3 

12 

8-11 

.42 

.16 

.58 

12-15 

.21 

.63 

16-20 

.27 

.69 

COSTS. 


185 


TABLE  XI.  —  Continued. 
CONCRETE  —  OCTAGONAL  SECTION. 


1 

2 

3 

4 

5 

6 

Safe  load. 

Circum- 
scribed 
diameter 
of  column. 

Height  of 
column. 

Cost  of  con- 
crete per 
foot  height 
of  column. 

Cost  of 
steel  per 
foot  height 
of  column. 

Total  cost 
per  foot 
height  of 
column. 

Tons. 

Inches. 

Feet. 

51.0 

13 

8-10 

$0.50 

$0.16 

$0.66 

11-14 

.21 

.71 

15-19 

.27 

.77 

20 

.33 

.83 

59.0 

14 

8-10 

.58 

.16 

.74 

11-13 

.21 

.79 

14-18 

.27 

.85 

19-20 

.33 

.91 

67.8 

15 

8 

.66 

.16 

.82 

9-12 

.21 

.87 

13-16 

.27 

.93 

17-20 

.33 

.99 

77.0 

16 

8 

.76 

.16 

.92 

9-11 

.21 

.97 

•^ 

12-15 

.27 

1.03 

16-19 

.33 

1.09 

20 

.42 

1.18 

87.0 

17 

8 

.85 

.16 

1.01 

9-11 

.21 

1.06 

12-14 

.27 

1.12 

15-18 

.33 

1.18 

19-20 

.42 

1.27 

97.5 

18 

8-10 

.96 

.21 

1.17 

11-13 

.27 

1.23 

14-17 

.33 

1.29 

18-20 

.42 

1.38 

109.0 

19 

8-9 

1.06 

.21 

1.27 

10-13 

.27 

1.33 

14-16 

.33 

1.39 

17-20 

.42 

1.48 

186 


HANDBOOK   ON    REINFORCED    CONCRETE. 


TABLE  XI.  —  Continued. 
CONCRETE  —  OCTAGONAL  SECTION. 


1 

2 

3 

4 

5 

6 

Safe  load. 

Circum- 
scribed 
diameter 
of  column. 

Height  of 
column. 

Cost  of  con- 
crete per 
foot  height 
of  column. 

Cost  of 
steel  per 
foot  height 
of  column. 

Total  cost 
per  foot 
height  of 
column. 

Tons. 

Inches. 

Feet. 

120.0 

20 

8-9 

$1.18 

$0.21 

$1.39 

10-12 

.27 

1.45 

13-15 

.33 

1.51 

16-19 

.42 

1.60 

20 

.50 

1.68 

145.0 

22 

8 

1.43 

.21 

.64 

9-11 

.27 

1.70 

12-14 

.33 

1.76 

15-17 

.42 

1.85 

18-20 

.50 

1.93 

173.5 

24 

8-10 

1.71 

.27 

1.98 

11-12 

.33 

2.04 

13-15 

.42 

2.13 

16-19 

.50 

2.21 

20 

.61 

2.32 

203.2 

26 

8-9 

2.00 

.27 

2.27 

10-11 

.33 

2.33 

12-14 

.42 

2.42 

15-18 

.50 

2.50 

19-20 

.61 

2.61 

235.0 

28 

8 

2.31 

.27 

2.58 

9-11 

.33 

2.64 

12-13 

.42 

2.73 

14-16 

.50 

2.81 

17-20 

.61 

2.92 

270.0 

30 

8 

2.64 

.27 

2.91 

9-12 

.33 

2.97 

13-15 

.42 

3.06 

16-18 

.50 

3.14 

19-20 

.61 

3.25 

PROPORTIONS    OF    CONCRETE    MIXTURES.      187 


TABLE  XII.  —  Amounts  of  Cement,  Sand,  and  Stone  Required 
for  Concrete  Mixtures  of  Various  Proportions. 

CONCRETE  WITH  25-INCH  STONE. 


Proportions  of  mixture. 

Required  for  1  cubic  yard. 

Cement. 

Sand. 

Stone. 

Cement. 

Sand. 

Stone. 

Stone. 

Barrels. 

Cu.  yards. 

Cu.  yards. 

Tons. 

1 

1 

2.0 

2.72 

0.41 

0.83 

1.31 

1 

1 

2.5 

2.41 

0.37 

0.92 

1.40 

1 

1 

3.0 

2.16 

0.33 

0.98 

1.49 

1 

1.5 

2.5 

2.16 

0.49 

0.82 

1.14 

1 

1.5 

3.0 

1.96 

0.45 

0.89 

1.22 

1 

1.5 

3.5 

1.79 

0.41 

0.96 

1.31 

1 

1.5 

4.0 

1.64 

0.38 

1.00 

1.38 

1 

2.0 

3.0 

1.78 

0.54 

0.81 

1.02 

1 

2.0 

3.5 

1.66 

0.50 

0.88 

1.11 

1 

2.0 

4.0 

1.53 

0.47 

0.93 

1.18 

1 

2.0 

4.5 

1.43 

0.43 

0.98 

1.28 

1 

2.5 

3.5 

1.51 

0.58 

0.81 

.93 

1 

2.5 

4.0 

1.42 

0.54 

0.87 

1.02 

1 

2.5 

4.5 

1.33 

0.51 

0.91 

1.09 

1 

2.5 

5.0 

1.26 

0.48 

0.96 

1.15 

1 

2.5 

5.5 

1.18 

0.44 

0.99 

1.20 

1 

3.0 

4.0 

1.32 

0.60 

0.80 

.89 

1 

3.0 

45 

1.24 

0.57 

0.85 

.95 

1 

3.0 

5.0 

1.17 

0.54 

0.89 

1.03 

1 

3.0 

5.5 

1.11 

0.51 

0.93 

1.09 

1 

3.0 

6.0 

1.06 

0.48 

0.97 

1.15 

1 

3.5 

5.0 

1.11 

0.59 

0.85 

.91 

1 

3.5 

5.5 

1.06 

0.56 

0.89 

.98 

1 

3.5 

6.0 

1.00 

0.53 

0.92 

1.04 

1 

3.5 

6.5 

0.96 

0.51 

0.95 

1.09 

1 

3.5 

7.0 

0.91 

0.49 

0.98 

1.14 

188      HANDBOOK   ON   REINFORCED   CONCRETE. 


TABLE  XII.  —  Amounts  of  Cement,  Sand,  and  Stone. 
CONCRETE  WITH  STONE  |-!NCH  AND  UNDER. 


Cont'd. 


Proportions  of  mixture. 

Required  for  1  cubic  yard. 

Cement. 

Sand. 

Stone. 

Cement. 

Sand. 

Stone. 

Stone. 

Barrels. 

Cu.  yards. 

Cu.^ards. 

Tons. 

1 

1 

2.5 

2.10 

0.32 

0.80 

1.51 

1 

1 

3.0 

1.89 

0.29 

0  86 

1  58 

1 

1 

3.5 

1.71 

0.26 

0.91 

1.64 

1 

1 

4.0 

1.55 

0.24 

0.94 

1.70 

1 

1.5 

3.0 

1.71 

0.39 

0.78 

1.36 

1 

1.5 

3.5 

1.57 

0.36 

0.83 

1.42 

1 

1.5 

4.0 

1.46 

0.33 

0.88 

1.49 

1 

1.5 

4.5 

1.34 

0.31 

0.91 

1  53 

1 

1.5 

5.0 

1.24 

0.28 

0.94 

1.55 

1 

2.0 

3.5 

1.44 

0.44 

0.77 

1.25 

1 

2.0 

4.0 

1.34 

0.41 

0.81 

1.31 

1 

2.0 

4.5 

1.26 

0.38 

0.86 

1.38 

1 

2.0 

5.0 

1.17 

0.36 

0.89 

1.42 

1 

2.0 

6.0 

1.03 

0.31 

0.94 

1.53 

1 

2.5 

4.0 

1.24 

0.47 

0.75 

1.18 

1 

2.5 

4.5 

1.16 

0.44 

0.80 

1.24 

1 

2.5 

5.0 

1.10 

0.42 

0.83 

1.29 

1 

2.5 

5.5 

1.03 

0.39 

0.86 

1.36 

1 

2.5 

6.0 

0.98 

0.37 

0.89 

1.40 

1 

2.5 

7.0 

0.88 

0.33 

0.93 

1.44 

1 

3.0 

5.0 

1.03 

0.47 

0.78 

1.11 

1 

3.0 

5.5 

0.97 

0.44 

0.81 

1.24 

1 

3.0 

6.0 

0.92 

0.42 

0.84 

1.29 

1 

3.0 

6.5 

0.88 

0.40 

0.87 

1.35 

1 

3.0 

7.0 

0.84 

0.38 

0.89 

1.38 

1 

3.0 

7.5 

0.80 

0.37 

0.91 

1.40 

1 

3.0 

8.0 

0.76 

0.35 

0.93 

1.44 

1 

3.5 

6.0 

0.88 

0.46 

0.80 

1.20 

1 

3.5 

6.5 

0.83 

0.44 

0.82 

1.25 

1 

3.5 

7.0 

0.80 

0.43 

0.85 

1.26 

1 

3.5 

7.5 

0.76 

0.41 

0.87 

1.31 

1 

3.5 

8.0 

0.73 

0.39 

0.89 

1.36 

1 

3.5 

8.5 

0.71 

0.38 

0.91 

1.37 

1 

3.5 

9.0 

0.68 

0.36 

0.62 

1.42 

COMPAKISON   OF   MIXTURES.  189 

DESCRIPTION  OF  TABLE  XIII. 

This  table  has  for  a  purpose  to  compare  various 
proportions  of  mixture  or  mixes  as  regards  strength. 
For  a  basis  by  which  all  other  mixes  are  compared, 
a  1-1.5-3  mix  was  taken  and  called  100  per  cent 
efficient. 

Column  2  considers  that  the  strength  of  the  mix 
depends  upon  the  amount  of  cement,  and  that  the 
effect  of  the  cement  is  positive  in  regard  to  affect- 
ing strength.  Hence,  all  other  mixes  are  given  in 
percentages  of  strength,  calling  the  1-1.5-3  mix 
unity,  determined  as  just  stated. 

Column  3  considers  that  the  strength  of  the  mix 
varies  as  the  absence  of  the  aggregate,  and  that 
the  effect  of  the  aggregate  is  negative  as  affecting 
strength.  Accordingly,  all  other  mixes  are  given 
in  percentages  of  strength,  considering  the  1-1.5-3 
mix  the  basis. 


190        HANDBOOK   ON   REINFORCED   CONCRETE. 


TABLE  XIII.  —  Relative  Strength  of  Different  Proportions  of 

Mixture. 


1 

2 

3 

Proportion  of 
mixture. 

Deduced  by  amount 
of  cement. 

Deduced  by  amount 
of  aggregate 

1—1,5—3.0 

1.00 

1.00 

1—1.5—3.5 

.92 

.90 

1—1.5—4.0 

.85 

.82 

1—2—3.5 

.85 

.82 

1—2—4.0 

.78 

.75 

1-2-4.5 

.74 

.69 

1—2.5-4.0 

.73 

.69 

1—2,5—4.5 

.68 

.64 

1-2.5—5.0 

.64 

.60 

1-3-50 

60 

.56 

1—3—5.5 

.57 

.53 

1-3-60 

.54 

.50 

1-3.5-6  0 

52 

.48 

1-3.5-6  5 

.49 

.45 

1-35—7  0 

.47 

.43 

PAET  IT. 

DESIGNS  OF  REINFORCED  CONCRETE 
TRUSSES. 


191 


TRUSSED  ROOFS. 

THE  growing  demand  for  boiler  houses,  forge 
shops,  foundries,  dye  houses,  and  such  classes  of 
buildings  that  will  successfully  withstand  deteri- 
oration or  destruction  from  the  effects  of  gases, 
vapors,  or  fire,  warrants  a  brief  chapter  on  the 
design,  cost,  and  construction  details  of  reinforced 
concrete  trussed  roofs.  Up  to  the  present  time 
this  kind  of  construction  is  the  only  one  that  can 
be  conscientiously  recommended  to  successfully 
resist  the  effects  of  the  agencies  mentioned  above. 
Let  it  not  be  understood  that  the  classes  of  roofs 
named  before  are  the  only  ones  to  which  this 
system  is  applicable.  To  the  contrary,  no  limita- 
tion can  be  placed  on  the  scope  of  its  use  in  cases 
where  final  cost,  permanency,  and  low  insurance 
rates  are  to  be  considered. 

No  doubt  an  important  reason  why  its  use  has 
been  looked  upon  with  such  distrust  and  ill-favor, 
is  because  of  the  fussy  construction  details  which 
add  considerably,  and  often  with  restriction,  to 
the  first  cost,  by  way  of  form  work,  temporary 
shoring,  and  inconvenience  to  handling  materials, 
thereby  impeding  progress,  and  prohibiting  econ- 
omy. Much  of  this  difficulty  can  be  lessened  or 
overcome  by  adhering  to  some  of  the  details 
hereafter  mentioned. 

193 


194       HANDBOOK    ON   REINFORCED    CONCRETE. 


TRUSS  SKELETON. 

First  of  all,  a  brief  outline  is  given  of  truss 
members  that  may  be  successfully  and  economi- 
cally molded  outside  of  their  ultimate  locations, 
or  in  other  words,  apart  from  the  truss.  These 
pieces  may  be  formed  exactly  to  dimensions,  or 
may  be  fitted  with  bolts  or  any  necessary  future 
iron  work,  and  this  with  every  assurance  that 
when  erected  in  place,  such  bolts  or  iron  work  will 
be  properly  spaced  for  the  part  it  has  to  play  in 
the  building.  Secondly,  these  pieces  being  formed 
on  or  near  terra  firma,  can  receive  all  due  atten- 
tion when  pouring.  Thirdly,  all  shoring  or  bracing 
which  would  be  necessary  were  the  piece  molded 
in  place,  can  be  done  away  with,  since  the  piece 
is  self-supporting,  after  having  set  a  reasonable 
length  of  time,  and  hence  a  saving.  Fourthly, 
pieces  thus  molded  are,  or  should  be,  free  from 
sag,  which  so  often  occurs  when  monolithically 
poured,  and  are  therefore  free  from  eccentric  load- 
ing, and  no  part  overstressed  through  negligence 
of  inspection.  Fifthly,  such  members  can  be 
erected  as  inexpensively  as  can  wooden  ones,  and 
can  be  supported  on  the  forms  which  mold  the 
monolithic  parts  without  other  shoring  than  would 
be  necessary  for  said  molds. 

The  principal  parts  that  can  be  treated  thus  are 
the  diagonal  braces,  which  are  always  in  compres- 
sion when  in  place.  The  design  of  these  may  be 
successfully  treated  along  the  following  lines. 


TRUSSED   ROOFS.  195 

First  of  all,  these  braces  should,  if  rectangular  or 
square  in  section,  contain  four  rods  or  bars,  one 
in  or  near  every  corner,  and  these  of  such  size  as 
to  render  a  sufficient  moment  of  resistance  about 
the  central  axis  that  offers  the  least  radius  of 
gyration,  to  enable  the  piece  to  be  raised  into 
place  with  the  lashing  at  any  point  along  its 
length  without  causing  cracks.  If  circular  or 
octagonal  in  section,  use  eight  rods.  Secondly, 
the  length  of  the  braces  should  be  2  or  3 
inches  greater  than  the  neat  distance  required 
between  chords,  thus  allowing  a  tie  of  1  or  1J 
inches  into  each  chord.  In  addition  to  this  tie, 
the  four  rods  previously  mentioned  should  project 
4  to  8  inches  beyond  either  end  of  the  brace,  and 
these  projections,  when  the  surrounding  parts  are 
poured,  serve  to  form  a  monolithic  mass  with  the 
whole.  These  braces  may  be  designed  to  carry 
pillow  blocks,  supporting  shafting,  by  molding  in 
a  web  between  the  brace  and  its  adjoining  ver- 
tical tie,  into  which  web  may  be  anchored  hook 
bolts  for  receiving  the  pillow  blocks.  In  a  similar 
manner,  webs  may  be  formed  to  support  piping, 
or  to  accommodate  any  features  required.  Again 
when  purlin  braces  are  required,  either  to  decrease 
the  section  of  the  purlin,  or  to  longitudinally  brace 
the  lower  chords  of  the  main  trusses,  these  may  be 
successfully  formed  by  outside  molding.  As  it 
often  becomes  convenient  to  hang  shafting  parallel 
to  the  axes  of  the  main  trusses,  such  braces  seem 
especially  adapted  for  receiving  it  by  casting  webs 


196      HANDBOOK    ON   REINFORCED    CONCRETE. 

between  them  and  the  vertical  tie  members  of  the 
main  trusses.  These  braces  should  be  designed  as 
stated  under  diagonal  braces. 

All  other  parts  of  the  roof  frame,  comprising  the 
upper  and  lower  chords  of  the  main  trusses,  all 
vertical  ties,  as  well  as  all  purlins  and  rafters, 
should  be  formed  in  situ. 

In  the  following  tables,  giving  the  designs  of 
various  trusses  to  meet  certain  requirements,  it 
will  be  noted  that  two  sizes  have  been  given  for 
both  the  upper  and  lower  chords.  The  sizes 
marked  "Reinforcement  Sizes"  should  be  used 
merely  to  refer  back  to  similar  sizes  under  "  Beam 
and  Girder  Designs"  in  Part  III,  to  pick  out  the 
steel  sections  required  to  withstand  the  bending 
moment  brought  about,  in  the  case  of  upper 
chords,  by  a  uniformly  distributed  dead  and  live 
loading,  including  their  own  weights,  over  the 
particular  span.  In  the  case  of  lower  chords,  the 
reinforcement  is  merely  to  withstand  the  bending 
moment  due  to  their  own  weights  uniformly  dis- 
tributed over  the  spans  designated.  After  paying 
due  attention  to  continuous  girder  effects,  as 
treated  in  Part  III,  and  equally  applicable  here, 
no  other  reinforcement  except  that  to  resist  shear 
is  required  in  these  parts. 

Purlins  and  rafters  should  be  treated  as  beams, 
the  reinforcement  for  the  same  being  found  by 
referring  the  sizes  given  to  corresponding  ones  in 
Part  III,  bearing  in  mind  the  effect  of  continuity. 

In  the  tables  following,  the  areas  of  steel  sections 


TRUSSED    ROOFS.  197 

are  given  for  the  truss  rods  or  bars  in  the  vertical 
tension  members.  In  treating  this,  the  most  im- 
portant feature  of  the  design,  may  call  forth  vari- 
ous opinions.  It  is  suggested  from  a  practical 
standpoint,  to  use  round  rods  with  threaded  ends 
and  nuts,  having  flat  plate  bearing  washers  at 
each  end.  These  plates,  to  develop  by  compres- 
sion of  the  concrete,  the  safe  tensile  stress  in  the 
rod,  should  have  a  net  bearing  area  on  the  con- 
crete twenty  times  the  area  of  the  rod.  The  upper 
bearing  plate  should  be  bent  to  conform  to  the 
A  shape  of  the  upper  chord,  should  be  located  as 
near  the  upper  surface  as  practicable,  and  above 
a  layer  of  rods,  the  total  area  of  which,  combined 
with  the  concrete  and  steel  section  below,  will 
care  for  half  the  shearing  stress  developed  by  the 
safe  tension  in  the  truss  rod.  Table  III,  Part  III, 
gives  safe  shearing  forces  under  three  conditions, 
which  the  net  section  of  chord  under  the  bearing 
plate  will  resist  with  no  other  reinforcement  than 
that  required  in  the  chord  to  withstand  bending. 
When  further  reinforcement  is  required,  it  may  be 
designed  in  accordance  with  the  data  given  in 
Table  III,  Part  III,  and  this  supplied  as  just 
stated,  below  the  bearing  plate.  Again,  should 
this  reinforcement  just  determined,  prove  inade- 
quate to  care  for  the  tensile  stress  in  the  upper 
fibers  over  the  rods,  as  required  by  the  tables  on 
"Beams  having  Fixed  Ends,"  it  (the  reinforce- 
ment) should  be  further  increased.  Needless  to 
say,  the  bearing  area  of  the  upper  bent  plate  pre- 


198 


HANDBOOK  ON  REINFORCED  CONCRETE. 


viously  referred  to,  should  be  the  horizontally  pro- 
jected area.  The  lower  bearing  plate  should,  of 
course,  be  located  below  the  steel,  in  the  under- 
side of  the  lower  chord.  The  steel  section  here, 
if  the  occasion  requires,  should  be  increased  as 
stated  before,  so  that  the  safe  shearing  force 
either  side  of  the  truss  rod  will  develop  half  the 
safe  tensile  stress  of  the  rod.  Previous  to  pouring 
the  lower  chord,  the  truss  rods  with  their  lower 
bearing  plates  should  be  supported  in  place,  and 
later  molded  monolithically  with  the  lower  chord. 
The  truss  rods  should  then  be  surrounded  with  a 
form  of  square  section  having  bevelled  corners, 
and  of  a  size  equal  to  the  width  of  the  lower 
chord.  Just  as  soon  as  the  concrete  in  the  lower 
chord  has  set  sufficiently  to  resist  the  static  head, 
due  to  the  mass  of  plastic  concrete  above,  these 
forms  should  be  filled  in  around  the  truss  rod  with 
cement,  and  the  truss  completed.  In  the  four 
corners  of  these  vertical  tension  members,  should 
be  placed  rods  of  light  section  to  prevent  shrink- 
age cracks  between  these  members  and  the  upper 
and  lower  chords.  Consequently,  they  should  pro- 
trude far  enough  into  the  chords  to  obtain  the 
adhesion  necessary  to  develop  their  safe  tensile 
stress,  or  be  anchored.  The  combined  area  of 
these  rods  should  be  such  as  to  resist  by  tension 
the  contraction  due  to  the  evaporation  of  water 
from  the  vertical  members.  This  will  vary,  de- 
pending upon  the  plasticity  of  the  concrete  when 
poured,,  and  may  be  somewhat  overcome  by  using 


TRUSSED    ROOFS. 


199 


a  rather  dry  concrete  well  rammed  in  place,  and 
by  keeping  the  surface  moistened  with  water  after 
removing  the  forms  so  as  to  keep  it  from  setting 
faster  than  the  thicker  masses  in  the  chords.  In 
the  absence  of  experiments,  this  part  of  the  design 
can  be  carried  out  by  approximation  only,  but 
the  approximation  can  be  kept  within  bounds 
when  we  know  the  percentage  of  free  water  in 
the  concrete,  over  that  required  by  chemical  action, 
to  the  whole  mass,  since  the  shrinkage  is  in  direct 
proportion  to  this  percentage,  and  especially  when 
the  precautions  before  named  are  regarded. 

The  upper  bearing  plate  should  not  be  put  on 
until  the  concrete  has  reached  the  level  in  the 
upper  chord  to  receive  the  rods  under  the  plate. 
After  these  latter  have  been  placed  and  properly 
covered  with  a  stiff  cement,  the  plate  may  be 
inserted  over  the  end  of  the  rod  and  screwed  down 
firmly,  and  bedded  by  means  of  the  nut  above. 
Needless  to  say,  at  the  apex  of  the  truss,  the  rods 
under  the  plate  should  be  bent  to  suit  the  chord, 
and  also  the  bearing  plates.  The  vertical  mem- 
bers at  each  panel  point  should  be  similarly 
treated. 

As  before  mentioned,  due  regard  must  be  paid 
to  continuity  over  panel  points.  Accordingly,  the 
tension  thus  caused  by  bending,  should  be  cared 
for  by  rods  in  the  upper  side  of  both  chords  at 
these  points. 

Particularly  should  the  shear  caused  on  either 
side  of  the  panel  points  in  both  chords  be  treated 


200   HANDBOOK  ON  REINFORCED  CONCRETE. 

with  no  little  concern,  as  these  are  the  weakest 
points  in  the  design  if  not  properly  considered, 
both  in  the  design  and  in  the  workmanship. 
Accordingly,  at  all  such  points,  longitudinal  shear 
bars  should  be  inserted  on  either  side  of  the  panel 
points  to  care  for  the  longitudinal  shear  along 
the  neutral  axis  as  well  as  the  varying  longi- 
tudinal shear  between  the  neutral  axis  and  the 
upper  and  lower  layers,  as  treated  in  Part  III. 

In  cases  where  there  is  but  one  span  of  trusses 
over  the  width  of  the  building,  and  the  ends  of 
these  rest  on  the  outside  walls,  in  order  to  prevent 
the  tendency  of  the  upper  chord  to  shear  by  the 
lower  chord  or  produce  an  excessive  thrust  on  the 
outside  walls,  it  is  suggested  to  insert  a  rod  fas- 
tened at  one  end  around  the  first  truss  or  panel 
point  rod  from  the  support,  the  other  end  to  be 
threaded  and  supplied  with  a  nut  and  bearing 
plate.  This  plate  should  have  an  area  equal  to 
the  difference  in  areas  between  the  concrete  and 
steel  sizes  given  for  the  lower  chord,  and  should 
be  located  over  the  wall  at  a  point  to  receive  the 
thrust  from  the  upper  chord.  The  size  of  the  rod 
just  mentioned  should  be  one-twentieth  that  of 
the  bearing  plate,  and  its  location  should  be  at 
the  center  of  the  lower  chord.  This  provision  is 
not  necessary  at  a  bearing  where  trusses  extend 
in  both  directions. 


TRUSSED  ROOFS.  201 

ROOF  (PROPER). 

In  order  to  minimize  the  excessive  dead  load  of 
a  roof  that  has  to  withstand  a  given  loading, 
Table  XIV  has  been  drawn  up  for  such  special 
usage. 

For  light  roof  frames,  and  where  light  live  loads 
may  be  figured  on,  wooden  plank,  either  of  hard 
pine,  or  white  pine,  are  practicable  and  economical. 
For  white  pine  may  be  substituted  Northern  or 
Canadian  pine,  fir,  or  spruce.  To  render  the 
exposed  surface  fire-resisting,  a  cement  plaster,  of 
varying  thickness,  is  applied  to  the  underside  of 
the  plank.  This  plaster  is  held  on  by  metal  lath 
or  expanded  metal  fastened  directly  to  the  plank, 
or  to  furring  strips  on  the  plank.  Any  danger 
considered  imminent  from  dry  rot  may  be  ob- 
viated by  supplying  a  sufficient  number  of  small 
vent  holes  through  the  plaster.  To  surely  guard 
against  decay  from  the  above  source,  it  is  well  to 
kyanize  the  planks  before  putting  them  in  place. 
Kyanizing  is  especially  adapted  to  spruce  lumber, 
and  will  serve  as  a  double  precaution  against  rot, 
should  moisture  in  any  way  get  through  the 
plaster.  The  plank  may  be  held  down  by  spiking 
them  into  a  dovetailed  nailing  piece  let  into  the 
upper  chord  flush  with  its  upper  surface. 

The  cost  of  concrete  roofs  may  be  lessened  to 
some  extent  by  casting  them  in  slabs  of  a  length 
equal  to  the  bay,  and  of  a  width  suitable  for 
handling,  and  raising  into  place.  These  may  be 


202        HANDBOOK   ON   REINFORCED    CONCRETE 

fastened  to  the  upper  chord  by  clips  driven  into 
a  dovetailed  wooden  nailing  piece  as  mentioned 
above.  Each  slab  should  be  fastened  down  before 
the  adjoining  slab  is  placed.  To  produce  the  best 
results,  each  slab  should  be  so  formed  as  to  break 
all  joints  at  right  angles  to  the  trusses  or  bearings 
by  halving  the  lap  of  one  onto  that  of  the  other. 
When  molding,  clips  should  be  left  projecting 
from  the  underside  of  the  slabs  and  anchored 
around  the  lower  reinforcement  in  the  slabs. 
Before  raising  to  place,  a  very  light  metal  lath, 
expanded  metal  or  latticed  wire,  should  be  at- 
tached to  the  underside  of  the  slab  by  means  of 
the  clips  already  mentioned.  This  serves' as  a  key 
to  hold  on  a  plaster  coat  of  cement,  which  should 
be  added  in  one  thin  coat  over  the  entire  under- 
side surface  of  the  roof  to  give  a  desired  finish 
and  to  protect  the  metal  fastenings.  As  a  poor, 
but  economical  substitute,  the  plaster  finish  may 
be  omitted,  and  the  slabs  bedded  in"  cement  mortar 
at  the  bearings  and  lapped  joints,  afterwards  cut- 
ting a  V-joint  between  each  slab  with  a  chisel 
and  tool.  This  will  reduce  the  cost  given  in 
Table  XlVa  about  ten  cents  per  square  foot. 

DESCRIPTION  OF  TABLE  XIV. 

Table  XIV  is  drawn  up  to  give  special  roofs  to 
meet  special  requirements.  To  obtain  the  great- 
est strength  for  the  least  weight  of  material  has 
been  the  particular  object  sought. 


ROOF   TRUSSES. 


Line  1  gives  the  gross  loading  per  square 
foot  to  carry  which  the  roofs  have  been  designed. 
Line  2  gives  the  net  loading  which  equals  the 
live  loading  after  the  dead  weight  of  the  roof 
itself  has  been  deducted.  The  remainder  of  the 
table  will  explain  itself. 

TABLE  XIV. 


8-  Foot  Span. 

1.    Gross  load,  square  foot. 

50 

75 

100 

75 

100 

(Lbs.) 

2.    Net  load,  square  foot. 

25 

37.5 

50 

50 

75 

(Lbs.) 

3.    Thickness  plank.    (In.) 

2.5W.P. 

2.5W.P. 

3W.P. 

4.    Thickness  plaster.    (In.) 

1.5 



1.5 

1* 

6.    Thickness         concrete. 

(In.) 

3 

4 

6.    Steel  in  comp.     Square 

inch  per  lineal  foot. 

.28 

7.    Steel        in         tension. 

Square  inch  per  lineal 

foot. 

.65 

.5 

10-Foot  Span. 

1.    Gross  load,  square  foot. 

50 

75 

100 

75 

100 

(Lbs.) 

2.   Net  load,  square  foot. 

25 

37.5 

50 

50 

75 

(Lbs.) 

3.    Thickness  plank.    (In.) 

2.5W.P. 

3W.P. 

3H.P. 

4.    Thickness  plaster.  (In.) 

1.5 

.^.  . 



li 

1 

5.   Thickness        concrete. 

(In.) 

3 

4 

6.    Steel  in  comp.    Square 

inch  per  lineal  foot. 

64 

4 

7.    Steel  in  tension.  Square 

inch  per  lineal  foot. 

1.01 

.9 

204        HANDBOOK    ON    REINFORCED    CONCRETE. 
TABLE  XIV.  —  Continued. 


12-Foot 

Span, 

1.   Gross  load,  square  foot. 

50 

75 

100 

75 

100 

(Lbs.) 

2.   Net  load,  square  foot. 

25 

37.5 

50 

50 

75 

(Lbs.) 

3.   Thickness  plank.    (In.) 

3  W.P. 

3H.P. 

4H.P. 

4.   Thickness  plaster.  (In.) 

u 

1 

] 

5.   Thickness          concrete. 

4 

3 

4 

I 

(In.) 

6.   Steel  in  comp.     Square 

1  08 

91 

inch  per  lineal  foot. 

7.   Steel  in  tension.  Square 

1.45 

1.41 

inch  per  lineal  foot. 

14-Foot  Span. 

1.    Gross  load,  square  foot.     (Lbs.) 
2.    Net  load,  square  foot.     (Lbs.)  .  . 
3.   Thickness  plank.     (In.)  
4.   Thickness  plaster.     (In.)  
5.   Thickness  concrete.     (In.)  
6.   Steel  in  comp.     Square  inch  per 
lineal  foot. 
7.   Steel  in  tension.     Square  inch 
per  lineal  foot. 

50 
25 
3  H.P. 
1 

75 
37.5 

100 
50 

75 
25 
4  H.P. 
1 

4 
1.60 

1.97 

4 
1.36 

1.86 

16-Foot  Span. 

1.   Gross  load,  square  foot.     (Lbs.) 
2.    Net  load,  square  foot.     (Lbs.)  .  . 

50 
25 
4  H.P. 

f 

75 
37.5 

3 

2.28 

2.65 

100 
50 

4 
1.90 

2.40 

75 
50 
4  H.P. 
f 

4     Thickness  plaster      (In.)      .    ... 

5.   Thickness  concrete.     (In.)  
6.   Steel  in  comp.     Square  inch  per 
lineal  foot. 
7.   Steel  in  tension.     Square  inch 
per  lineal  foot. 



ROOF   TRUSSES. 
TABLE  XIV.  —  Continued. 


205 


18-  and  20-Foot  Span. 

1.   Gross  load,  square  foot. 

50 

75 

100 

75 

100 

(Lbs.) 

2.   Net  load,  square  foot. 

25 

37.5 

50 

50 

75 

(Lbs) 

3.    Thickness  plank.    (In.) 

2.5W.P. 

3W.P. 

5H.P. 

4.   Thickness  plaster.  (In.) 

1.5 

l| 

1 

5.    Thickness         concrete. 

3 

4 

(In.) 

6.    Steel  in  conap      Square 

64 

4 

inch  per  lineal  foot. 

7.    Steel  in  tension.  Square 

1  01 

9 

inch  per  lineal  foot. 

NOTE.  —  Spans  mentioned  above  as  18  and  20  feet  are 
actually  reduced  to  9  and  10  feet,  respectively,  by  means  of 
the  intermediate  rafters,  and  are  mentioned  as  such  only  to 
afford  a  ready  reference  when  using  Table  XVII.  Likewise, 
bays  of  24  and  30  feet  actually  give  spans  for  the  roofing  of 
but  8  and  10  feet,  respectively. 

DESCRIPTION  OF  TABLE  XlVa, 

This  table  gives  the  approximate  costs  of  roofs 
per  square  foot  of  projected  area  covered,  when 
constructed  of  the  materials  and  designed  as 
stated  in  Table  XIV.  All  costs  given  are  in  dol- 
lars or  fractional  parts  thereof. 

The  span  mentioned  under  Column  1  is  just  a 
reference  back  to  Table  XIV,  where  may  be 
found  the  amounts  of  steel  for  the  various  spans 
here  specified. 

These  costs  are  fair  averages  of  ordinary  cases. 
In  cases  where  the  average  working  conditions 
cannot  be  obtained,  allowance  must  be  made. 


206        HANDBOOK   ON   REINFORCED    CONCRETE. 


For  cases  where  wooden  plank  are  used,  two 
sets  of  costs  are  given  in  the  table.  The  first  is 
for  plain  lumber;  the  second  is  for  the  same  stock, 
but  kyanized. 

TABLE  XI Va.  —  Cost  in  Dollars. 


1 

2 

3 

4 

5 

6 

Formed 
in 
place. 

Slabs  set 
in 
place. 

Thickness  ot  plaster. 

t" 

1" 

li" 

U" 

Thickness  of  Concrete: 
3"  (8  ft.  span)  
3"  (10  ft.  span).  ... 
3"  (12  ft.  span).... 
3"  (14  ft.  span)  
3"  (16  ft.  span)  

Thickness  of  Concrete 
4"  (8  ft.  span)  
4"  (10  ft.  span)'  
4"  (12  ft.  span)  
4"  (14  ft.  span).... 
4"  (16  ft.  span)  

Thickness  of  Plank: 
2£"  W  P 

$0.40 
.45 
.52 
.60 
.72 

.45 
.53 
.61 
.68 
.79 

$0  38 
.40 
.47 
.53 
.63 

.39 

.45 
.52 
.58 
.67 

fO.34 
.36 

3  "  W  P 

$0  36 

3  "  W  P 

$0  32 

.39 

4  "  W  P 

$0  .  35 
.39 

.35 

DESCRIPTION  OF  TABLE  XV. 
This   table   is   drawn   up   to   furnish   complete 
designs  of  trusses,  of  the  type  here  shown  in  the 
sketch  for  various  bays  and  spans. 


ROOF   TRUSSES.  207 

Columns  2,  3,  and  4  give  sizes  of  upper  chords 
when  the  slope  of  the  truss  is  45  degrees.  The 
figures  in  the  upper  set  are  sizes  from  which  the 
reinforcement  may  be  determined  by  reference  to 


CENTER  OF  TRUSS 


a 

CENTER  OF  TRUSS 


ELEVATION 


tables  in  Part  III,  while  the  lower  set  gives  the 
concrete  sizes. 

Columns  5,  6,  and  7  are  similar  in  every  way  to 
columns  2,  3,  and  4,  giving  corresponding  sizes  for 
30  degrees  slope  trusses. 

Columns  8  to  10,  inclusive,  and  11  to  13,  inclu- 
sive, give  sizes  of  lower  chords,  and  are  similar 
to  columns  2  to  4  and  5  to  7,  respectively. 

Columns  14  to  16  contain  the  reinforcement 
sizes  from  which  the  steel  for  the  lower  chord  may 
be  determined  by  reference  to  the  corresponding 
sizes  in  Table  I,  Part  III. 

Columns  17  to  19  give  areas  in  square  inches  of 
truss  rods  for  the  corresponding  bays  and  spans 
noted. 


208        HANDBOOK   ON   REINFORCED    CONCRETE. 
TABLE  XV. 

25-Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

6X20 

7X20 
6X22 

7X22 
6X24 

7X24 
6X24 
7X24 
7X24 
8X24 

8  . 

5X18 
5.5X18 
5X20 
5.5X20 
6X20 
6.5X20 
6X22 
6.5X22 
6X22 
6.5X22 

6X20 
6.5X20 
6X22 
6.5X22 
6X24 
6.5X24 
7X24 
7.5X24 
7X24 
8X24 

6X22 
6.5X22 
6X24 
6.5X24 
7X26 
7.5X26 
7X26 
8X26 
7X28 
8X28 

5X16 
5.5X16 
5X18 
5.5X18 
5X18 
5.5X18 
5X20 
5.5X20 
6X20 
7X20 

5X18 
5.5X18 
5X20 
6X20 
6X20 
7X20 
6X22 
7X22 
6X24 
7X24 

10  
12  .... 

14  
16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10  
12 

3.5X10 
3.5X10 
4X12 
4.5X12 
4.5X12 

4X12 
4.5X12 
4.5X14 
6X12 
6X14 

4.5X12 
6X12 
6X14 
6X16 
7X16 

4X10 
4X10 
4X12 
5X12 
5X12 

4X12 
5X12 
5X14 
6.5X12 
7X14 

5X12 
6X12 
6.5X14 
7X16 
8X16 

14  

16  

Lower  Chord. 

Truss  Rod. 

14 

15 

16 

17       |       18 

19 

Reinforcement  Sizes. 

Area  in  sq.  in. 

8  
10  
12  

2.5X10 
2.5X10 
2.5X12 
3X12 
3X12 

2.5X12 
3X12 
3X14 
4X12 
4X14 

3X12 
4X12 
4X14 
4X1& 
5X16 

.20 
.20 
.25 
.31 
.31 

.24 
.30 
.36 
.40 
.51 

.30 
.36 
.47 

.58 
.66 

14  

16 

NOTE.  —  LTpper  figures  indicate  reinforcement  sizes, 
indicate  concrete  sizes. 


Lower  figures 


ROOF   TRUSSES. 
TABLE  XV.  —  Continued. 

30  Foot  Span. 


209 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

5X20 
5.5X20 
6X20 
6.5X20 
6X20 
6.5X20 
6X22 
7X22 
6X24 
7X24 

75 

6X20 
6.5X20 
6X22 

7X22 
6X24 
7X24 
7X24 
8X24 
7X26 
8X26 

100 

6X24 
7X24 
7X24 
8X24 
7X26 
8X26 
7X28 
8-X28 
8X28 
9.5X28 

8  

6X20 
6.5X20 
6X22 

6.5X22 
6X24 
6.5X24 

6X24 
6.5X24 
7X26 
7.5X26 

6X24 
6.5X24 

7X24 
7.5X24 
7X26 
7.5X26 
7X28 
7.5X28 
8X28 
9X28 

7X26 
7.5X26 
7X28 
7.5X28 
8X28 
9X28 
8X30 
9X30 
8X32 
9X32 

10       

12  
14  
16  .... 

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

4X12 
4X12 
5X12 
5X12 
5X14 

12 

13 

5.5X14 
6.5X14 
7X16 
8X16 
8X18 

8  
10 

3.5X12 
3.5X12 
4X12 
4.5X12 
4.5X14 

4X12 
4.5X12 
5.5X12 
5.5X14 
5.5X16 

4.5X14 
5.5X14 
5.5X16 
7X16 
7X18 

5X12 
5.5X12 
7X12 
7X14 
7X16 

12  
14  
16  

Lower  Chord. 

Truss  Rod. 

14 

15 

16 

17 

18 

19 

Reinforcement  Sizes. 

Area  in  sq.  in. 

8 

2.5X12 
2.5X12 
3X12 
3X12 
3X14 

3X12 
3X12 
4X12 
4X14 
4X16 

3X14 
4X14 
4X16 
5X16 
5X18 

.30 
.30 
.37 
.40 
.44 

.37 
.42 
.52 
.61 
.70 

.48 
.57 
.70 
.79 
.90 

10  
12  

14     ... 

16  

210       HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XV.  —  Continued. 
35-Foot  Span, 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  

6X24 
6.5X24 
7X26 
7.5X26 
7X28 
7.5X28 
7X28 
7.5X28 
8X28 
8.5X28 

7X28 
7.5X28 
8X28 
8.5X28 
8X30 
8.5X30 
8X32 
9X32 
9X32 
10X32 

8X28 
8.5X28 
8X32 
8.5X32 
9X32 
10X32 
9X34 
10X34 
9X36 
10X36 

6X20 
6.5X20 

6X22 
6.5X22 
6X24 
7X24 
7X24 
8X24 
7X26 
8X26 

6X24 
7X24 
7X26 
8X26 
7X26 
8X26 
8X28 
9X28 
8X30 
9X30 

7X26 
8X26 
7X28 
8X28 
8X28 
9X28 
8X32 
9X32 
8X32 
9.5X32 

10 

12  

14  ..,,  
16  ...    . 

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10  
12     .  . 

4X14 
4X14 
4X14 
4.5X14 
5.5X14 

4X14 
5.5X14 
5.5X14 
5.5X16 
7X16 

5.5X14 
5.5X16 
7X16 
7X18 
7X20 

4.5X14 
4.5X14 
5X14 
5X14 
6.5X14 

5X14 
6.5X14 
7X14 
7X16 
8X16 

6.5X14 
6.5X16 
8X16 
8X18 
8.5X20 

14  :  
16 

Lower  Chord. 

Truss  Rod. 

14 

15 

16 

17 

18 

19 

Reinforcement  Sizes. 

Area  in  sq.  in. 

8  
10  
12  •  

3X14 
3X14 
3X14 
3X14 
4X14 

3X14 
4X14 
4X14 
4X16 
5X16 

4X14 
4X16 
5X16 

5X18 
5X20 

.46 
.46 
.51 
.51 
.67 

.52 
.66 
.72 
.82 
.93 

.66 
.76 
.92 
1.05 
1.15 

14  

16  

ROOF    TRUSSES. 

TABLE  XV.  —  Continued. 
40-Foot  Span. 


211 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  
10             ... 

7X28 
7.5X28 
8X28 
8.5X28 
8X30 
8.5X30 
8X32 
8.5X32 
9X32 
9.5X32 

8X30 
8.5X30 
8X32 
8.5X32 
9X32 
9.5X32 
9X34 
10X34 
9X36 
10X36 

8X32 
8.5X32 
9X34 
10X34 
9X36 
10X36 
10X38 
11X38 
10X40 
11X40 

6X24 
6.5X24 
7X24 
8X24 
7X26 
8X26 
7X28 
8X28 
8X28 
9X28 

7X26 
8X26 
8X28 
9X28 
8X30 
9X30 
8X32 
9X30 
9X32 
10X32 

8X28 
9X28 
8X32 
9X32 
9X32 
10X32 
9X34 
10.5X34 
9X36 
10.5X36 

12 

14  

16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10 

5X16 
5X16 
5X16 
5.5X16 
5.5X16 

5.5X16 
5.5X16 
5.5X16 
7X16 
7X18 

5.5X16 
6.5X16 
7X16 
7.5X16 
8.5X20 

5.5X16 
5.5X16 
6X16 
6X16 
6.5X16 

6X16 
6.5X16 
7X16 
8X16 
8.5X18 

6.5X16 
8X16 
8.5X18 
8.5X20 
10X20 

12  

14 

16  

Lower  Chord. 

Truss  Rod. 

14       |       15 

16 

17 

18 

19 

Reinforcement  Sizes. 

Area  in  sq.  in. 

8    

4X16 
4X16 
4X16 
4X16 
4X16 

4X16 
4X16 
4X16 
5X16 
5X18 

4X16 
5X16 
5X18 
5X20 
6X20 

.74 
.74 
.80 
.80 

.87 

.80 
.87 
.94 
1.06 
1.32 

.87 
1.06 
1.32 
1.42 
1.66 

10  

12 

14  
16  

212        HANDBOOK   ON   REINFORCED    CONCRETE. 


TABLE  XV.  —  Continued. 

45-Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5         |        6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

8X30 
8.5X30 
8X32 
8  5X32 
9X32 
9.5X32 
9X34 
9  5X34 

75 

100 

9X36 
9  5X36 
10X38 
11  X38 
10X40 
11  X40 
11X42 
12X42 
11X44 
12X44 

50 

75 

100 

8  
10       ... 

9X32 
9.5X32 
9X36 
9  5X36 
10  X36 
11X36 
10X38 
11X38 
10X40 
11  X40 

7X26 
7.5X26 
7X28 
7.5X28 
8X28 
9X28 
8X30 
9X30 
9X32 
10X32 

8X28 
9X28 
8X32 
9X32 
9X32 
10X32 
9X34 
10X34 
9X36 
10X36 

8X32 
9X32 
9X34 
10X34 
9X36 
10X36 
10X36 
10.5X36 
10X40 
10.5X40 

12 

14  

16       

10X36 
10.5X36 

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10 

GX18 
6X18 
6X18 
6.5X18 
6.5X18 

6X18 
6.5X18 
6.5X18 
7X18 
7X20 

6.5X18 
7X18 
7X18 
7.5X18 
8.5X22 

6.5X18 
6.5X18 
7X18 
7.5X18 
7.5X18 

7X18 
7.5X18 
8X18 
8.5X18 
8.5X20 

7.5X18 
9X18 
8.5X20 
10X20 
10X22 

12       

14  

16           .    . 

Lower  Chord. 

Truss  Rod. 

14 

15 

16 

17 

18 

19 

Reinforcement  Sizes. 

Area  in  sq.  in. 

8  

5X18 
5X18 
5X18 
5X18 
5X18 

5X18 
5X18 
5X18 
5X18 
5X20 

5X18 
5X18 
5X20 
6X20 
6X22 

1.10 
1.10 
1.18 
1.28 
1.28 

.18 
.28 
.35 
.48 
.59 

1.28 
1.52 
1.59 

1.88 
2.06 

10  
12  

14  

16  

ROOF  TRUSSES. 


213 


TABLE  XV.  —  Continued. 
50-Foot  Span. 


Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8 

9X34 
9.5X34 
9X36 
9.5X36 
10X36 
10.5X36 
10X38 
10.5X38 
10X40 
'0.5X40 

10X36 

10.5X36 
10X40 
10.5X40 
11X40 
11.5X40 
11X42 
12X42 
11X44 
12X44 

10X40 
10.5X40 
11X42 
12X42 
11X44 
12X44 
12X44 
13X44 
13X48 
14X48 

8X28 
8.5X28 
8X30 
8.5X30 
9X32 
10X32 
9X34 
10X34 
10X36 
11X36 

8X32 
9X32 
9X34 
10X34 
9X36 
10X36 
10X38 
11X38 
10X40 
11X40 

9X34 
10X34 
10X36 
11X36 
10X40 
11X40 
11  X42 
12.5X42 
11X44 
12.5X44 

10 

12  

14  
16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  

6X20 
6X20 
6X20 
6X20 
7.5X20 

6.5X20 
6.5X20 
6.5X201 
7X20 
8.5X20 

6.5X20 
8X20 
8X20 
8.5X20 
8.5X24 

6.5X20 
6.5X20 
7X20 
7.5X20 
7.5X20 

7X20 
7.5X20 
7.5X20 
8X20 
9.5X20 

7.5X20 
8X20 
9.5X20 
10X22 
10.5X24 

10  

12  
14  

16 

Lower  Chord. 

Truss  Rod. 

14 

15 

16 

17 

18 

19 

Reinforcement  Sizes. 

Area  in  sq.  in. 

8  
10  
12  
14  

5X20 
5X20 
5X20 
5X20 
5X20 

5X20 
5X20 
5X20 
5X20 
6X20 

5X20 
5X20 
6X20 
6X22 
6X24 

.36 
.36 
.46 
.56 
.56 

1.46 
1.56 
1.56 
1.70 
1.98 

1.56 
1.& 
1.98 
2.28 
2.66 

16  

214      HANDBOOK   ON    REINFORCED    CONCRETE. 

DESCRIPTION  OF  TABLE  XVa. 

Under  this  table  is  compiled  data  for  estimating 
the  weights  of  various  truss  skeletons  of  the  type 
shown  under  Table  XV,  for  different  bays  and 
spans.  The  weights  given  are  in  pounds  per 
square  foot  of  projected  area  covered.  These 
weights  do  not  include  the  weight  of  the  roof 
proper.  Use  may  be  made  of  this  data  in  design- 
ing columns  or  other  supports  to  receive  the 
trusses,  or  in  estimating  the  yardage  of  their 
volume  for  cost  purposes,  since  approximately 
4,000  pounds  of  homogeneous  concrete  equals  one 
cubic  yard.  After  the  yardage  of  concrete  is 
known,  the  quantities  of  constituents  forming  the 
concrete  may  be  figured  by  reference  to  Table 
XII,  Part  III,  when  the  proportions  of  mixture 
are  known. 


ROOF  TRUSSES. 


215 


TABLE  XVA.  —  Weight  of  Truss  Skeleton  per  Square  Foot  of 

Area  Covered. 

25-Foot  Span. 


1 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.) 

30°  Slope. 
Load  sq.  ft.  (Ibs.) 

50 

75 

100 

50 

75 

100 

8  

23 
20 
20 
19 
17 

30 
27 
25 
24 
23 

33 
31 
31 
29 

28 

19 
16 
14 
14 
14 

21 
21 
20 
19 
19 

29 
26 
25 
23 
23 

10 

12 

14  

16 

Average  

20 

26 

30 

15 

20 

25 

30-Foot  Span. 


8  

30 

36 

44 

23 

28 

35 

10 

25 

32 

39 

21 

25 

33 

12  

24 

30 

39 

18 

24 

31 

14 

21 

28 

37 

18 

24 

29 

16  

22 

29 

35 

17 

23 

30 

24 

31 

39 

19 

25 

32 

35-Foot  Span. 


8  

37 

46 

54 

31 

38 

49 

10 

35 

43 

50 

26 

40 

42 

12   

31 

38 

49 

25 

34 

40 

14  

27 

37 

45 

24 

33 

39 

16 

27 

37 

43 

25 

32 

37 

Average  

31 

40 

48 

26 

35 

41 

216 


HANDBOOK   ON   REINFORCED   CONCRETE. 


TABLE  XVa.  —  Continued. 
40-Foot  Span. 


1 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.) 

30°  Slope. 
Load  sq.  ft.  (Ibs.) 

50 

75 

100 

50 

75 

100 

8  .  .  .  
10  

49 
44 
38 
35 
34 

59 
50 
45 
44 
42 

48 

62 
61 
54 
53 
52 

36 
32 
30 

27 
26 

44 
41 
37 
33 
34 

52 
48 
46 
43 
41 

12 

14  
16 

Average 

40 

56 

30 

38 

46 

45-Foot  Span. 


8 

61 
52 
47 
43 
43 

49 

71 
63 
59 
54 
50 

59 

79 
75 
65 
63 
61 

45 
38 
36 
33 
33 

54 
"49 
45 
41 
38 

61 
58 
51 
47 
46 

10 

12  
14 

16          

Average  

69 

37 

45 

52 

50-Foot  Span. 

8      

75 
63 
57 
51 
49 

87 
76 
68 
64 
60 

95 
90 
79 
73 
76 

53 
44 
44 
40 
39 

62 
56 
49 
49 
45 

72 
64 
61 
61 
58 

10 

12        ... 

14   

16 

59 

71 

83 

44 

52 

63 

ROOF  TRUSSES.  217 

DESCRIPTION  OF  PLOTS. 

In  general,  each  set  of  plots  has  been  drawn  up 
to  render  a  ready  means  of  determining  the  cost 
of  the  type  of  truss  skeleton  per  square  foot  of 
projected  area  covered  by  the  different  bays  and 
spans.  These  values  should  agree  very  approxi- 
mately with  general  straightforward  cases,  and 
they  are  sufficiently  accurate  for  estimating  com- 
pleted work.  In  special  cases  they  should  be 
modified  to  suit  the  case  at  hand. 

The  plots  serve  a  ready  means  of  comparing 
different  types  of  truss  skeleton  from  a  financial 
standpoint.  To  bring  out  this  point  two  dia- 
grams have  been  plotted :  one  comparing  the  types 
shown  under  Tables  XVI  and  XVIII;  the  other, 
those  shown  under  Tables  XVII  and  XVIII.  It 
may  be  seem  that,  for  like  conditions,  the  type 
shown  under  Table  XVIII  is  more  economical  than 
either  of  the  other  two,  and  again,  that  type 
"XVI"  is  cheaper  than  "XVII." 

The  cost  per  square  foot  of  projected  area  of 
type  XVIIc  is  about  10  per  cent  greater  than  that 
of 'types  XVII  to  XVII6,  while  that  of  XVIId  is 
about  20  per  cent  greater  than  that  of  XVII  to 
XVII6  for  like  bays  and  corresponding  spans. 


218 


HANDBOOK  ON  REINFORCED  CONCRETE. 


8  .FT-  BAY 

CURVES  SHOWING  THE'RELATION 
OF  COST  TO  SPAN 

(For  Truss' see  Table  15) 


W^ 

c 

^ 

0 

^, 

^ 

0) 

^ 

^ 

an  O 

^ 

x* 

^ 

CO 

^ 

•* 

^ 

^ 

^ 

^> 

jj 

^^ 

••* 

^ 

-^ 

co 

I 

_^j 

k^ 

^, 

^^ 

^^ 

!_ 

9 

5Q 

•^ 

^ 

-* 

^ 

.  —  ' 

' 

O 

ws 

j. 

j 

^ 

k-- 

__ 

.  — 

\« 

I 

^ 

i' 

L-^- 

-^ 

^J 

UJ 

^ 

• 

^ 

^J 

^ 

*^ 

1 

0 

3 

i 

^- 

•^* 

o- 

M 

^ 

§ii 

^-* 

^50 

£ 

-^ 

"U£ 

/ 

Q. 

0 

x 

5 

<u 

/ 

c 

ftm 

^ 

^ 

nO 

x 

,  —  ' 

x 

^x 

' 

x 

.E 

in    •> 
* 

/ 

1 

x 

1 

/ 

tri 

X 

X 

x 

O 

°?n 

^ 

X 

X 

f 

? 

O 

,  — 

X 

x 

j 

X 

x 

/ 

> 

^ 

<£ 

-n 

< 

^ 

•* 

/ 

x 

Q- 

9 

^ 

^ 

•^ 

• 

X1 

x 

x 

00 

^ 

$ 

^it 

^ 

(1 

,x 

-^ 

^ 

t 

^x 

Q_ 

^r 

bj 

^" 

! 

^j 

•^ 

00 

| 

f 

^ 

—  • 

i 

e 

^H 

•" 

0> 

5 

' 

c 

•^ 

o 

0  n 

! 

2 

5 

3 

0 

3 

5 

4 

3 

4J 

5C 

1 

Span  in  Feet 


ROOF    TRUSSES. 


219 


10  FT.  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN 

(For  Type  of  Truss  see  Table  15) 


4C  ^ 

0 

0) 

^«- 

Q. 

' 

fX 

X- 

^ 

_^. 

•  — 

x* 

-^ 

X-* 

i  — 

O 

, 

|X 

— 

^" 

oo 

-r- 

~ 

X- 

x^ 

^* 

^~ 

^--' 

* 

on  ° 

^ 

iX 

^- 

-— 

,  —  * 

fis 

[7 

+*- 

-— 

. 

\<- 

X 

" 

i 

— 

^* 

M- 

n1 

** 

^> 

^- 

1 

k 

^* 

^^ 

^. 

. 

9 

x» 

0 

r*- 

-- 

<*• 

W 

-^   - 

.^*" 

>~> 

n 

Q. 

g 

/ 

^x 

t^ 

/ 

0) 

o 

't 

/ 

0  o 

c/> 

/ 

/ 

c 

m 

't 

/ 

X 

+J 

S 

X 

0 

»- 

X 

^ 

^ 

O 

U_ 

x 

s 

X 

^ 

X 

X 

^ 

X 

X 

+J 

x 

^ 

^ 

X 

^a 

^ 

^ 

X 

w~ 

r 

V 

X 

^ 

--- 

^ 

20 

.n 

^ 

^ 

•^ 

j 

^ 

<* 

> 

^« 

* 

..^ 

0 

i 

X 

> 

, 

^i 

-^ 

X 

** 

c 

^ 

*-* 

O 

n 

O    0 

25 


30 


35  40 

Span  in  Feet 


45 


50 


220      HANDBOOK   ON    REINFORCED    CONCRETE. 


1 2  FT.  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN 

(For  Type  of  Tmss  see  Table  15) 


25 


30  35  40 

Span  in  Feet 


50 


ROOF    TRUSSES. 


14  FT.  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN, 

For  Truss  see  Table  15 ) 


40  <^s 

c 

0 

CD 

Q. 

x^ 

S 

^ 

' 

°O 

^* 

**• 

X 

^ 

I 

,-*• 

>** 

^^ 

--1 

O 

p 

sQ 

**• 

^** 

^" 

^. 

-" 

20  \±, 

p,s 

* 

**** 

—  • 

\** 

-- 

1 

-—  • 

.-— 

^~~ 

H- 

_j 

1 

• 

,**" 

^ 

^ 

_^ 

.^^ 

cr 

i 

j 

—  • 

<=!<" 

> 

*—  — 

w 

>?o 

o 

T 

—  • 

IU  Jn 

c 

I 

Q. 

V) 

Q 

C 

On 

<Jj  ^ 

If) 

J 

c 

X 

•M 

o 

^ 

O 

^  30 

S 

,x 

O 

^ 

, 

? 

*J 

^* 

, 

S 

. 

,a 

-^ 

^ 

S 

_^, 

cr 

V-t 

*• 

! 

^ 

** 

^*- 

-* 

oc 

> 

i> 

1 

-^- 

** 

** 

*** 

** 

„*-*- 

-^* 

.  —  ' 

^ 

^ 

> 

•^" 

f 

^ 

^ 

I 

^ 

**• 

,  — 

(i 

^x 

^ 

c 

-< 

^ 

,»- 

^^ 

— 

^  10 

|- 

to 

O 

o 

2 

3 

6 

J 

s 

pa 

n 

J 
in 

b 
f 

"e 

el 

t 

^ 

) 

4 

b 

b 

0 

222      HANDBOOK    ON    REINFORCED    CONCRETE. 


1  6  FT,  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN. 

( For  Truss  see  Table  15 ) 


30  35  40 

Span  in  Feet 


ROOF   TRUSSES. 


223 


DESCRIPTION  OF  TABLE  XVI. 

This  table  treats  the  type  of  truss  shown  as 
does  Table  XV  its  type.  By  reference  to  the 
description  of  the  latter,  this  table  will  be  readily 
understood.  No  further  mention  need  be  made 
except  in  cases  where  excessively  long  spans  cause 


CENTER  Of  TRUSS 


CENTER  OF  TRUSS 


PLAN 

TYPE  16 


ELEVATION 


diagonal  braces  longer  than  thirty  times  the  least 
dimension  of  the  brace  section,  in  which  cases, 
when  the  reinforcement  will  not  carry  the  tension 
caused  by  the  eccentric  loading,  either  the  rein- 
forcement should  be  increased,  or  the  unsupported 
length  diminished  by  struts  or  braces  of  small 
section. 

NOTE.  —  For  reinforcement  in  upper  chord,  use  that  re- 
quired in  Table  XV  for  one-half  the  span  given  here. 

NOTE.  —  The  reinforcement  sizes  of  lower  chord  are  the 
same  for  both  the  45°  slope  and  the  30°  slope. 


224     HANDBOOK:  ON  REINFORCED  CONCRETE. 


TABLE  XVI. 

40-Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  
10  

4X16 
5X16 
5X16 
6X16 
5X18 
6X18 
5X18 
6X18 
5X20 
6X20 

5X18 
6X18 
5X18 
6.5X18 
5X20 
6.5X20 
6X20 
7.5X20 
6X22 
7.5X22 

5X20 
6.5X20 
6X20 
7.5X20 
6X22 
7.5X22 
6X22 
8X22 
6X24 
8X24 

4X14 
5X14 
4X16 
5.5X16 
5X16 
6.5X16 
5X16 
7X16 
5X18 
7X18 

5X16 
6.5X16 
5X16 
7X16 
5X18 
7X18 
5X20 
7X20 
5X20 
7.5X20 

5X18 
7X18 
5X20 
7X20 
5X20 
7.5X20 
6X20 
9X20 
6X22 
9X22 

12  

14  
16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10 

4X16 
5X16 
4X16 
5X16 
4X16 
5X16 
4X16 
5X16 
4X16 
5.5X16 

4X16 
5X16 
4X16 
5.5X16 
4X16 
5.5X16 
5X16 
7X16 
5X18 
7X18 

4X16 
5.5X16 
5X16 
7X16 
5X18 
7X18 
5X20 
7X20 
6X20 
8X20 

5.5X16 

6X16 

6.5X16 

5.5X16 

6.5X16 

8X18 

12  

6X16 

7X16 
7X16 
7.5X16 

8X16 
8.5X20 
10X20 

14  
16 

6X16 
6.5X16 

Area  of  Truss 
Rod  (sq.  in.). 

Diagonal  Braces. 

1 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Bay 

(feet). 

Load  sq.ft.  (Ibs.). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30    SloDe. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

50 

75 

100 
4X7 

8  

1.38 

1.98 

2.58 

4X3 

4X5 

4X6 

4X4 

4X6 

10  

1.68 

2.43 

3.22 

4X4 

4X6 

5X6 

4X5 

4X7 

5X7 

12  

1.78 

2.88 

3.88 

4X5 

4X7 

5X7 

4X5 

4X8 

5X9 

14  

2.28 

3.37 

4.48 

4X5 

5X6 

5X8 

4X6 

5X8 

5X10 

16  

2.58 

3.88 

5.13 

4X6 

5X7 

6X8 

4X7 

5X9 

6X10 

ROOF    TRUSSES. 


225 


TABLE  XVI.  —  Continued. 
50- Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  
10  

6X18 
6X20 
7X20 
7.5X22 
7.5X22 

7X20 
7.5X22 
7.5X24 
8.5X26 
9X26 

7.5X22 
7.5X24 
9X26 
9X26 
9X28 

6.5X16 
6.5X18 

7X18 
7X20 
8X20 

7X.18 
8X20 
8.5X20 
8.5X22 
8.5X24 

8X20 
8.5X22 
8.5X^4 
9X24 
10.5X24 

12  
14  
16 

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10 

5X20 
6X20 
5X20 
6X20 
5X20 
6X20 
5X20 
6.5X20 
5X20 
6.5X20 

5X20 
6X20 
5X20 
6.5X20 
5X20 
6.5X20 
5X20 
7X20 
6X20 
8X20 

5X20 
6.5X20 
5X20 
7.5X20 
6X20 
8X20 
6X22 
8X22 
6X24 
8.5X24 

6.5X20 

7X20 

7.5X20 

6.5X20 
7X20 

7.5X20 
7.5X20 

8.0X20 
9.5X20 

12  
14  

7.5X20 

8X20 

10X22 

16 

7.5X20 

9.5X20 

10X24 

Area  of  Truss 
Rod  (sq.  in.). 

Diagonal  Braces. 

1 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Bay 

(feet). 

Load  sq.  ft.  (Ibs.) 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

50 

75 

100 
5X7 

8  

1.8 

2.6 

3.4 

5X3 

5X5 

5X6 

5X4 

5X6 

10  

2.2 

3.2 

4   10 

5X4 

5X6 

5X7 

5X5 

5X7 

5X9 

12  

2.6 

3.8 

5.0 

5X5 

5X7 

6X7 

5X6 

5X8 

6X9 

14  

3.0 

4.4 

5.8 

5X5 

5X8 

6X9 

5X6 

5X9 

6X10 

16  

3.4 

4.9 

6.6 

5X6 

6X7 

6X10 

5X7 

6X9 

6X12 

226 


HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVI.  —  Continued. 
60-Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8 

7X20 
7X22 
7.5X24 
7.5X24 
7.5X26 

7X24 
8.5X24 
8.5X26 
8.5X28 
10X28 

8X26 
8.5X28 
10X28 
10X30 
11.5X32 

6.5X20 

7.5X20 
8X20 
8X22 
8X24 

8X20 
8X22 
8.5X22 
9.5X24 
10X26 

8X24 
9.5X24 
10X26 
10X28 
11.5X28 

10  

12  
14  

16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

8  
10 

6X24 
7X24 
6X24 
7X24 
6X24 
7X24 
6X24 
7.5X24 
6X24 
7.5X24 

6X24 
7X24 
6X24 
7.5X24 
6X24 
7.5X24 
6X24 
8X24 
6X24 
8X24 

6X24 
7.5X24 
6X24 
8X24 
6X24 
8X24 
7X24 
9.5X24 
7X24 
10X24 

7.5X24 

7.5X24 

8X24 
8.5X24 

8.5X24 
9X24 

12  
14  
16           .... 

8X24 

8.5X24 

9.5X24 

8X24 
8.5X24 

9X24 
9.5X24 

11X24 
11.5X24 

Area  of  Truss 
Rod  (sq.  in.). 

Diagonal  Braces. 

1 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Bay 

(feet). 

Load  sq.ft.  (Ibs.). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

50 

75 

100 

8  

2.4 

3.3 

4.2 

6X3 

6X4 

6X6 

6X4 

6X5 

6X7 

10  

2.9 

4.0 

5.1 

6X4 

6X5 

6X7 

6X5 

6X7 

6X9 

12  

3.3 

4.7 

6.0 

6X4 

6X6 

6X8 

6X5 

6X8 

6X10 

14  

3.8 

5.3 

7.0 

6X5 

6X7 

7X8 

6X6 

6X9 

7X10 

16  

4.2 

6.0 

7.9 

6X6 

6X8 

7X9 

6X7 

6X10 

7X12 

ROOF   TRUSSES. 


227 


TABLE  XVI.  —  Continued. 
70- Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  
10 

7X24 
8X26 
8.5X28 
8.5X28 
9.5X28 

8X28 
9.5X28 
10X30 
10X32 
11X32 

9.5X28 
9.5X32 
11X32 
11X34 
11.5X36 

7.5X20 
7.5X22 
8X24 
9X24 
9.5X26 

8X24 
9X26 
9.5X26 
10.5X28 
11X30 

9X26 
9.5X28 
11X28 
11X32 
11.5X32 

12  
14 

16 

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

Reinforcement  Size, 
7  X  28  for  whole  span. 

8  
10  
12 

8X28 
8X28 
8X28 
8.5X28 
8.5X28 

8X28 
8.5X28 
8.5X28 
9X28 
9X28 

8.5X28 
9X28 
9X28 
9.5X28 
10X28 

8.5X28 
8.5X28 
9X28 
9X28 
9.5X28 

9X28 
9.5X28 
10X28 
10X28 
10.5X28 

9.5X28 
10X28 
10.5X28 
11X28 
11.5X28 

14  
16  

Area  of  Truss 
Rod  Uq.  in.). 

Diagonal  Braces. 

1 

14 

15    |    16 

17 

18 

19 

20 

21 

22 

Bay 

(feet). 

Load  sq.  ft.  (Ibs.). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

50 

75 

100 

8  

3.05 

4.10 

5.15 

7X3 

7X4 

7X5 

7X3 

7X5 

7X7 

10  

3.58 

4.89 

6.20 

7X3 

7X5 

7X6 

7X4 

7X6 

7X8 

12  

4.10 

5.68 

7.25 

7X4 

7X6 

7X8 

7X5 

7X7 

7X10 

14  

4.58 

6.59 

8.30 

7X5 

7X7 

7X9 

7X6 

7X8 

7X11 

16  

5.15 

7.25 

9.35 

7X5 

7X8 

7X10 

7X7 

7X10 

7X13 

228       HANDBOOK   ON   REINFORCED    CONCRETE. 

TABLE  XVI.  —  Continued. 
80- Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  
10  
12 

8X28 
9X28 
9.5X30 
9.5X32 
10.5X32 

9.5X30 
9.5X32 
10.5X32 
11X34 
11X36 

9.5X32 
11X34 
11X36 
12X38 
12.5X40 

7.5X24 
9X24 
10X28 
lOXcO 
11  X3k 

9X26 
10X28 
11.5X32 
11.5X34 
13X36 

10.5X28 
11.5X32 
12X36 
13.5X36 
13.5X40 

14  
16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

Reinforcement  Size, 
8  X32  for  whole  span. 

8  

9X32 
9X32 
9X32 
9.5X32 
9.5X32 

9X32 
9.5X32 
9.5X32 
10X32 
10X32 

9.5X32 
10X32 
10.5X32 
10.5X32 
11  X32 

9.5X32 
9.5X32 
10X32 
10X32 
10.5X32 

10X32 
10.5X32 
10.5X32 
11  X32 
11.5X32 

10.5X32 
11X32 
11.5X32 
12X32 
13X32 

10 

12  
14  
16  

Area  of  Truss 
Rod  (sq.  in.)- 

Diagonal  Braces. 

1 

14 

15 

16         17          18 

19 

20 

21          22 

Bay 

(feet). 

Load  sq.  ft. 

45°  Slope. 
0"*)       Load  sq.  ft    (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100        50 

75 

100 

50 

75          100 

8  
10  
12  
14.    ... 
16  

3.8 
4.4 
5.0 
5.6 
6.2 

5.0 
5.9 

6.8 

7.7' 
8.6 

6.2      8X3 
7.4      8X3 
8.6      8X4 
9.8      8X4 
11.0      8X5 

8X4 
8X5 
8X6 
8X6 
8X7 

8X5 
8X6 
8X7 
8X8 
8X10 

8X3 
8X4 
8X5 
8X5 
8X6 

8X5      8X6 
8X6      8X8 
8X7      8X9 
8X8      8X11 
8X9      8X12 

ROOF    TRUSSES. 


229 


TABLE  XVI.  —  Continued. 
90-Foot  Span. 


1 

Sizes  of  Upper  Ohor 

d. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  
10  
12 

9X30 
9X32 
10.5X32 
10.5X34 
12X36 

10.5X32 
10.5X36 
11.5X36 
12X38 
12X40 

10.5X36 
12X38 
12X40 
13X42 
13.5X44 

8.5X26 
X28 
10X28 
10X30 
11.5X32 

10X28 
10X32 
11.5X32 
12X34 
12X36 

10.5X24 
11.5X33 
12X36 
13.5X36 
13.5X40 

14  
16  

Sizes  of  Lower  Chord. 

8 

9 

10 

11 

12 

13 

Reinforcement  Size, 
9  X36  for  whole  span. 

8  
10 

10X36 
10X36 
10X36 
10.5X36 
10.5X36 

10X36 
10.5X36 
10.5X36 
11X36 
11X36 

10.5X36 
11X36 
11X36 
11.5X36 
12X36 

10.5X36 
10.5X36 
11X36 
11X36 
11.5X36 

11  X36 
11.5X36 
12X36 
12X36 
12.5X36 

11.5X36 
11.5X36 
12.5X36 
13X36 
13.5X36 

12  
14  
16  

Area  of  Truss 
Rod  (sq.  in.). 

Diagonal  Braces. 

1 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Bay 

(feet). 

Load  sq.  ft.  (Ibs.). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

30 

75 

100 

50 

75 

100 

50 

75 

100 

8  

4.7 

6.1 

7.4 

9X3 

9X4 

9X5 

9X3 

9X5 

9X6 

10  

5.4 

7.1 

8.8 

9X3 

9X5 

9X6 

9X4 

9X6 

9X7 

12  

6.1 

8.2 

10.2 

9X4 

9X5 

9X7 

9X5 

9X7 

9X9 

14  

6.8 

9.2 

11.6 

9X4 

9X6 

9X8 

9X5 

9X8 

9X10 

16  

7.4 

10.1 

12.8 

9X5 

9X7 

9X9 

9X6 

9X9 

9X12 

230      HANDBOOK   ON    REINFORCED   CONCRETE. 


TABLE  XVI.  —  Continued. 
100-Foot  Span. 


1 

Sizes  of  Upper  Chord. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°    slope. 
Load  sq.  ft.  (Ibs.). 

30°    slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

8  

10X34 
11X36 
11.5X36 
11.5X38 
11.5X40 

11.5X36 
11.5X40 
12.5X40 
13X42 
13X44 

11.5X40 
12.5X42 
13X44 
14.5X44 
15.5X48 

9.5X28 
10.5X30 
11  X32 
11X34 
12.5X36 

10X32 
11.5X34 
11.5X36 
13X38 
13X40 

11.5X34 
13X36 
13X40 
14.5X42 

15X44 

10  
12  
14  

10 

Sizes  of  Lower  Chord. 

8 

g 

10 

11 

12 

13 

Reinforcement  Size, 
10  X38  for  whole  span. 

8  

11X38 
11X38 
11X38 
11.5X38 
11.5X38 

11X38 
11.5X38 
11.5X38 
12X38 
12.5X38 

11.5X38 
12X38 
12X38 
12.5X38 
13X38 

11.5X38 
11.5X38 
12X38 
12.5X38 
13X38 

12X38 
12.5X38 
13X38 
13.5X38 
14X38 

12.5X38 
13X38 
13.5X38 
14X38 
15X38 

1  )  
12  
14 

10  

Area  of  Truss 
Rod  (sq.  in.). 

Diagonal  Braces. 

1 

14 

15 

16 

17 

18 

19 

20 

21 

22 

Bay 

(feet). 

Load  sq.  ft.  Clbs.). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 
7.1 

100 

50 

75 

100 

50 

75 

100 

8  

5.6 

8.6 

10X3 

10X4 

10X5 

10X3 

10X4 

10X6 

10  

6.4 

8.2 

10.1 

10X3 

10X4 

10X6 

10X4 

10X5 

10X7 

12  

7.1 

9.4 

11.6 

10X4 

10X5 

10X7 

10X4 

10X6 

10X8 

14  

7.9 

10.2 

13.1 

10X4 

10X6 

10X8 

10X5 

10X7 

10X10 

16  

8.6 

11.6 

14.6 

10X5 

10X7 

10X9 

10X6 

10X8 

10X11 

ROOF   TRUSSES. 


231 


DESCRIPTION  OF  TABLE  XVIa. 

Like  Table  XVa,  this  table  has  computed  values 
of  the  weights  of  various  truss  skeletons,  of  the 
type  shown  under  Table  XVI,  per  square  foot  of 
projected  area  for  different  bays  and  spans.  Like 
uses  may  be  made  of  this  data,  as  stated  under 
the  description  of  Table  XVa. 

TABLE  XVIa.  —  Weight  of  Truss  Skeleton  per  Square  Foot 
of  Area  Covered. 

40-Foot  Span. 


1 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

g 

26 
23 
21 
19 
18 

32 
28 
26 
26 
25 

38 
36 
33 
31 
30 

23 
21 
20 
18 
17 

30 
26 
24 
22 
21 

34 
32 

28 
30 
30 

10  
12 

14 

16      

Average  .  . 

21 

27 

34 

18 

25 

31 

50-Foot  Span. 

8 

37 
32 
29 
28 
25 

44 
40 
36 
36 
34 

50 
45 
45 
41 
40 

34 
35 
26 
24 
23 

39 
37 
32 
30 
29 

47 
42 
40 
37 
37 

10  
12  

14 

16  

Average  

30 

38 

44 

28 

33 

41 

60-Foot  Span. 

g 

49 

42 
38 
33 
30 

55 
51 
44 
41 
40 

65 
59 
53 
51 
48 

45 
39 
34 
31 
29 

52 
53 
38 
37 
36 

59 
52 
48 
46 
44 

10   

12 

14      .        . 

16    

Average  

38 

46 

55 

36 

43 

50 

. 

232      HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVIa.  —  Continued. 

70-Foot  Span. 


1 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

75 
63 
60 
57 
52 

8  
10 

62 
56 
51 
45 
43 

73 
68 
60 
55 
52 

85 
74 
69 
64 
60 

56 
48 
43 
39 
39 

64 
60 
52 
49 

47 

12                             

14 

16                                    .    . 

Avftraffe  .  . 

51 

62 

70 

45 

54 

61 

80- Foot  Span. 


g 

81 

93 

99 

69 

80 

92 

10         

69 

79 

92 

60 

71 

84 

12        

62 

71 

81 

58 

69 

79 

14 

56 

66 

76 

52 

62 

74 

16        

53 

60 

73 

50 

62 

71 

64 

74 

84 

58 

69 

80 

90-Foot  Span. 


g 

100 

113 

122 

87 

98 

109 

10  
12 

83 
75 

98 

87 

113 
97 

73 
65 

85 
78 

95 

87 

14 

75 

81 

92 

58 

71 

81 

16  

67 

73 

87 

57 

65 

76 

Average  

80 

90 

102 

68 

79 

90 

100-Foot  Span. 

8   

122 
106 
91 
83 

74 

136 
118 
100 
96 

88 

146 
131 
116 
108 
106 

103 
87 
78 
71 
69 

113 
101 
89 
85 

78 

127 
108 
101 
97 
91 

10 

12   

14  

16 

Average  

95 

108 

121 

82 

93 

105 

ROOF    TRUSSES. 


233 


8  FT.  BAV 

CURVES  -SHOWING  1  HE^RELATION 
OP  COST  TO  SPAN, 

.For  Type  of  Truss  see -Table.  16 


-  70 

X" 

/ 

60    c 

x 

o 

y 

o 

x' 

^ 

x1 

y 

/ 

\*  X 

x 

o 

£>r 

^x 

X         LL, 

,«j 

1       " 

y 

^**. 

JW 

x* 

/ 

/                -M 

^* 

t             IS 

/ 

S  3 

/ 

, 

'    ^ 

14 

-N^ 

'TTj 

/ 

o- 

2lE 

X* 

x^ 

V30  w 

X        J^X 

-^ 

o 

X          x* 

1°, 

^x 

2 

Q. 

XXX 

x  X      ^^     x  ^ 

i 

^/ 

/J 

-2 

?  1 

x^       X  "^ 

x    / 

> 

20  ^ 

0                     £5  *  ** 

^ 

/ 

^ 

z^ 

LL^            '     S[t  ?     ^ 

^ 

«>   1  Jf  "*     ' 

^    ^/ 

^ 

_.^. 

£40            ^ 

5 

/      y 

^ 

r-IQ     0 

II  Jj 

^; 

? 

k  7 

x^ 

_10  (J 

CT 

35 

? 

y 

'         ^X 

X 

*•  s 

^- 

3  * 

, 

*•  7 

CL  on 

^^Tt^ 

-    0 

w   3 

^     \%X      i 

/ 

^     ^^  o^-x 

<L) 

x        ^     ~p 

o                     x 

^             ^ 

X               X 

--  20      ^y7,,^ 

X  ** 

•£          Zgw-^ 

u          ^Si?f 

10 

1C 

40 


50 


60  70 

Span  in  Feet 


80 


90 


100 


234        HANDBOOK   ON    REINFORCED    CONCRETE. 


10  FT.  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN 

(For  Type  of  Truss  see  Table  16) 


90 

| 

DU  ^^ 

1 

V 

™  ® 

7 

^/ 

f 

V) 

/^          > 

c 

^ 

/ 

/ 

o 

0       ?n 

> 

40  °° 

o     /u 

/ 

^  ' 

c 

.  ~? 

~? 

O 

y 

^  ** 

/_ 

^ 

^ 

^  / 

S 

> 

(/) 

^> 

X 

S 

30  "c 

.Q 

<^ 

Is 

,  ^' 

^ 

y 

<u 

^^ 

^ 

^ 

3 

, 

/ 

O 

0    C 

s* 

X 

1^  X 

^ 

u  o 

^t' 

^Jf 

B 

o^ 

y           / 

*&    <D  en 

x 

sf 

~? 

X 

/ 

20  +-' 

O    QjJU 

? 

^> 

7 

rt    0 

^ 

^  ^ 

X 

^ 

Q- 

-M  W 

ft 

X  ' 

2 

^        / 

w 

H—  ° 

ii 

<A 

> 

^_ 

"o 

^  ^* 

p 

£ 

10    o 

s 

/ 

1      x 

i_    0 

<? 

vf 

> 

ts 

<D  H- 

^'/ 

n 

V 

^/ 

0 

3:  ^ 

0 

A 

•>  r 

o 

^ 

S 

X 

w  td/30 

^ 

'\ 

X 

X 

X 

' 

*/ 

1- 

' 

^' 

. 

#- 

0         on 

3^ 

X 

± 

^        20 

UJ 

^S 

^s 

o 

s 

s 

Q 

s 

°ir 

•»* 

50  60  70 

Span  in  Feet 


80 


90 


100 


ROOF   TRUSSES. 


235 


12  FT.  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN. 

(For  Type  of  Truss  see  Table  16) 


,' 

50^; 

x 

c 

^, 

o 

> 

^ 

^x 

in   a- 

70 

> 

x 

* 

*0   0 

• 

x 

co 

x 

x 

X 

X 

^ 

x 

>^  n 

r^ 

X 

S 

30  i- 

C60 

<• 

^  ' 

X1 

J. 

0 

0 

r 

S 

x 

•^ 

/ 

u_ 

<1> 

Y 

V- 

r 

I.  •' 

1 

x* 

x—  ^ 

Q. 

£,- 

> 

5 

X 

( 

^ 

X 

/ 

^J 

o 

^ 

HH 

•^ 

>/ 

*+- 

CObU 

J 

x' 

" 

^ 

^ 

,  ' 

0 

^ 

x 

2 

5 

^ 

/ 

w 

^f 

^, 

^ 

x* 

D^ 

X* 

/ 

/ 

^ 

u 

S 

.x 

*^ 

X- 

/ 

0) 

o  1Q 

, 

to 

^« 

** 

^ 

s 

x* 

in  ^ 

u_  i-u 

tf 

^x 

^x 

^ 

IU    CO 

-^ 

X 

,x 

c 

+j 

S 

x* 

X 

<u 

** 

^ 

^ 

U 

CTon 

V 

^ 

^x 

X 

Oc 

CO  -3U 

ff 

^ 

J 

v« 

x^ 

1_ 

x 

. 

CO 

. 

# 

X 

^ 

(r)x 

^ 

s 

0 

\k 

^ 

* 

ls 

^x  ' 

O 

X 

^ 

x 

^x 

t:  20 

^ 

^ 

x 

<s 

^ 

UJ 

>x 

^ 

X* 

ft 

x- 

^ 

c 

3 

X* 

pj 

to  10 

-r 

O 

4 

0 

5 

0 

6 

D 

70 

8 

0 

9 

z 

10 

0 

Span  in  Feet 


236        HANDBOOK    ON    REINFORCED    CONCRETE. 


<L) 

0.60 

<± 
CO 
V> 

tso 
o 


o 

Q-30 


20 


10 


14  FT.  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN. 

(For  Type  of  Truss  see  Table  16) 


?£ 


^ 


0,0.. 


50 


40 


30  Q. 
c> 

CO 

20? 


10" 


40 


50  60  70 

Span  in  Feet 


80 


90 


100 


ROOF   TRUSSES. 


237 


;eo 


50 


10 


16  FOOT  BAY 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN 

For  Type  of  truss.  see'Table  16 


i 


-f 


40 


40 


50 


60  70 

Span  in  Feet, 


90 


100 


238      HANDBOOK   ON   REINFORCED   CONCRETE. 

DESCRIPTION  OF  TABLE  XVII. 
The  type  of  truss  here  shown  is  treated  similarly 
to  those  shown  under  Tables  XV  and  XVI, 
giving  complete  designs  of  all  the  members.  The 
only  peculiarity  of  this  table  over  Table  XVI  is 
that,  to  reduce  the  roof  span  on  account  of  widen- 
ing the  bays,  intermediate  rafters  carried  on  pur- 
lins, have  been  interposed  as  the  sketch  will 
clearly  show.  It  has  been  figured  to  keep  the 
same  size  for  the  purlins  as  for  the  intermediates. 


CENTER  OF  TRUSS 


J 

< 

i 

z 
"      - 

,    RAFTERS 

z 
-> 

§ 

1 

„    1 

,    TRUSS    a 

PLAN 
TYPE  17 


ELEVATION 

To  do  so  the  span  of  the  purlin  can  be  but  one- 
half  that  of  the  intermediates  for  a  given  case, 
since  there  is  a  concentrated  load  on  the  former 
equal  to  the  uniformly  distributed  load  on  the 
latter.  To  reduce  the  span  of  the  purlins  the 
amount  just  stated,  purlin  braces  have  been 
figured  to  be  placed  diagonally  between  the  under- 
side of  the  purlins  and  their  adjacent  vertical  tie 
members  at  the  panel  points.  These  braces  serve 
as  sway  bracing  to  the  lower  chords  of  the  main 
trusses  as  well. 


ROOF    TRUSSES. 


239 


TABLE    XVII.  —  Sizes  of  Intermediates.     Sizes  of  Purlins. 
30-Foot  Span. 


Bay 

(feet). 

Upper  Chord.     Reinforcement  Sizes. 

45°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

18           .    . 

4X14 
4X16 

4X16 
5X16 

5X18 
5X18 

3X14 
3X14 

4X16 
4X16 

5X16 
5X16 

20  

40-Foot  Span. 


18 

5X18 
5X18 

5X20 
6X20 

6X22 
6X22 

4X16 
4X16 

5X16 
5X18 

5X20 
5X20 

20  

50-Foot  Span. 

18  
20  

6X20 
6X22 

6X24 

7X24 

7X26 

7X28 

5X16 

5X18 

5X20 
6X20 

6X22 
6X22 

60-Foot  Span. 

18  
20 

6X24 
7X24 

7X28 
7X28 

8X30 
8X30 

6X20 
6X20 

6X20 
6X24 

7X24 
7X26 

70-Foot  Span. 

18  

7X28 
8X28 

8X30 
8X32 

9X34 
9X34 

6X24 

6X24 

7X26 
7X26 

8X28 
8X28 

20  .  . 

30-Foot  Span. 


Bay 

(feet). 

Reinforce- 
ment 
Sizes,  any 
slope. 

Lower  Chord.     Concrete  Sizes. 

45°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  per  sq.  ft.  (Ibs). 

18  
2")  

2.5X12 
2.5X12 

50 

75 

100 

50 

75 

100 

4X12 
5X12 

5X12 
6X12 

6X12 
7X12 

6X12 
7X12 

7X12 
8X12 

9X12 
9X12 

40-Foot  Span. 


18  
20  

4X16 
4X16 

6X16 
6X16 

7X16 
7X16 

8X16 
8X*16 

7X16 
8X16 

9X16 
9X16 

10X16 
11  X16 

240       HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVII.  —  Continued. 
50- Foot  Span. 


Bay 

(feet). 

Reinforce- 
ment 
Sizes,  any 
slope. 

Lower  Chord.     Concrete  Sizes. 

45°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

12X20 
13X20 

18  
20  

6X20 
6X20 

8X20 
8X20 

9X20 
9X20 

10X20 
10X20 

9X20 
10X20 

10X20 
11  X20 

60-Foot  Span. 


18  
20  

6X24 
6X24 

8X24 
8X24 

9X24 
9X24 

10X24 
10X24 

9X24 
10X24 

11X24 
11  X24 

12X24 
13X24 

70-Foot  Span. 


18  
20  

7X28 
7X28 

9X28 
9X28 

10X28 
10X28 

11X28 
11X28 

10X28 
11X28 

12X28 
12X28 

13X28 
11X28 

30-Foot  Span. 


Bay 

(feet). 

Upper  Chord.     Concrete  Sizes. 

45°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  per  sq.  ft.  ()bs.«). 

50 

75 

100 

50 

75 

100 

10X16 
10  5X16 

18  
20  

6X14 
6X16 

7X16 
8X16 

8X18 
9X18 

6X14 
6X14 

8X16 
8X16 

40-Foot  Span. 


18  
20  

7X18 
8X18 

8X20 
9X20 

10X22 
10X22 

7.5X16 
8X16 

10X16 
10X18 

10.5X20 
11X20 

50- Foot  Span. 


18  
20  

9X20 
9X22 

9X24 
10X24 

11  X26 
12X28 

9.5X16 
9.5X18 

10X20 
11.5X20 

12.5X22 
13X22 

60-Foot  Span. 


18 

9  X24 

10  X28 

13X30 

10  5  X20 

12X20 

14X24 

20  

10X24 

11  X28 

13X30 

11X20 

12X24 

14X26 

70-Foot  Span. 


18  
20  

10X28 
12X28 

12X30 
12X32 

13X34 
13X34 

10X24 
10.5X24 

12.5X26 
14X26 

15X28 
15.5X28 

ROOF    TRUSSES. 


241 


TABLE  XVII.  —  Continued. 
30-Foot  Span.     Diagonal  Braces. 


Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.) 

50 

75 

10.0 

50 

75 

100 

18  
20  

4X6 
5X5 

5X7 
6X6 

6X8 

7X7 

6X6 
7X6 

7X7 

8X7 

9X9 
9X8 

40-Foot  Span. 


18 

6X6 
6X6 

7X7 
7X8 

8X8 
8X9 

7X7 
8X7 

9X8 
9X9 

10X10 
11X11 

20  

50-Foot  Span. 

18 

8X7 
8X7 

9X8 
9X9 

10X10 
10X11 

9X10 
10X10 

10X12 
11X12 

12X13 
13X13 

20  

60-Foot  Span. 

18  
20  

8X8 
8X9 

9X10 
9X12 

10X13 
10X14 

9X14 
10X14 

11X15 
11X17 

12X17 
13X17 

70-Foot  Span. 

18  
20 

9X10 
9X12 

10X12 
10X12 

11X14 
11X15 

10X15 
11X16 

12X17 
12X19 

13X20 
14X20 

30-Foot  Span.     Purlin  Braces. 

18  
20  

3X3 
3X3 

3X4 
3X4 

4X4 
4X4 

3X4 

3X4 

4X5 
4X5 

5X5 
5X5 

40-Foot  Span. 

18       .... 

4X4 
4X4 

5X5 
5X5 

X6 
X6 

5X5 
5X5 

6X6 
6X6 

6X8 
6X8 

20    ., 

50-Foot  Span. 

18 

5X5 

5X5 

6X6 
6X6 

7X7 
7X7 

6X6 
6X6 

7X8 
7X8 

7X10 
7X10 

20           .    . 

60-Foot  Span. 

18  

6X6 

6X6 

7X7 
7X7 

8X8 
8X8 

7X7 
7X7 

7X11 
7X11 

8X13 
8X13 

20 

70-Foot  Span. 

18  
20  

7X7 
7X7 

8X9 
8X9 

9X11 
9X11 

8X9 
8X9 

8X13 
8X13 

9X55 
9X15 

242      HANDBOOK   ON   REINFORCED   CONCRETE. 


TABLE  XVII.  —  Continued. 
30-Foot  Span.     Truss  Rods  at  Apex. 


18           .    . 

.18 
.92 

1.06 
1.37 

1.43 
1.74 

.93 
1.06 

1.36 
1.50 

1.77 
1.94 

20  

40-Foot  Span. 

18  
20  

1.34 
1.37 

1.78 
1.95 

2.36 
2.56 

1.42 
1.53 

2.01 
2.20 

2.60 

2.85 

50-Foot  Span. 

18  
20  

2.04 
2.18 

2.73 
3.00 

3.56 
4.04 

2.44 
2.70 

3.22 
3.66 

4.06 
4.56 

6:-Foot  Span. 

18  
20           .    . 

2.58 

2.87 

3.59 
3.90 

4.82 
5.20 

3.40 
3.82 

4.40 
4.86 

5.45 
6.00 

70-Foot  Span. 

18  

3.46 
4.02 

4.66 
6.07 

5.95 
6.33 

4.24 
4.94 

5.74 
6.34 

7.19 
7.79 

20 

30-Foot  Span.     Panel  Point  Rods. 

18 

.31 
.33 

.47 
.48 

.62 
.63 

.48 
.49 

.70 
.74 

.93 
.95 

20  

40-Foot  Span. 

18  
20 

.60 
.60 

.87 
.87 

1.14 
1.14 

.87 
.87 

1.28 
1.28 

1.67 
1.67 

50-Foot  Span. 

18  
20  

1.02 
1.02 

1.45 
1.45 

1.88 
1.88 

1.44 
1.44 

2.08 
2.08 

2.73 
2.73 

60-Foot  Span. 

18  
20  

1.40 
1.40 

1.89 
1.89 

2.58 
2.58 

2.03 
2.03 

2.95 
2.95 

3.83 
3.83 

70-Foot  Span. 

18  
20  .. 

2.03 
2.03 

2.87 
2.87 

3.70 
3.70 

2.76 
2.76 

3.99 
3.99 

5.16 
5.16 

ROOF   TRUSSES. 


243 


18-20  FT.  BAYS 

CURVES  SHOWING  THE  RELATION 
OF  COST  TO  SPAN 

(For  Type  of  Truss  see  Table  17) 


4U 

/ 

x 

x 

^ 

x 

^ 

x 

^ 

' 

c,C 

1-  , 

x- 

X 

9 

tj 

^ 

' 

x^ 

X 

X" 

0 

™ 

"X1 

x- 

•^ 

' 

x^ 

0 

X- 

" 

0 

^ 

x- 

^0 

_, 

x-1 

j 

^* 

XH 

•*" 

Q. 

^ 

x' 

b 

3 

x 

— 

_^- 

•^* 

' 

c 

O.  /m 

0  40 

x 

(/) 

x 

^ 

4 

o 

x 

s 

^ 

X 

x 

J 

^ 

.30 

X 

9." 

X 

x 

^ 

CT 

^ 

H 

x" 

^ 

' 

x 

(0 

a^j 

x 

,v 

X^ 

" 

x- 

x 

t- 

> 

/ 

X" 

' 

X 

05  20 

/ 

XI 

,1 

X 

, 

7 

1 

> 

-M 

x 

^x 

PI 

^ 

x' 

05 

s 

^ 

x- 

n  1D 

-J 

X* 

x' 

1 

n 

x- 

^ 

^_, 

o 

O  n 

Sf 


30  40  50  60 

Span  in  Feet 


70 


244      HANDBOOK  ON   REINFORCED   CONCRETE. 

DESCRIPTION  OF  TABLE  XVIIa. 
Under  this  table  may  be  found  values  of  the 
weights  per  square  foot  of  projected  area  covered 
of  the  type  of  truss  skeletons  shown  in  the  de- 
scriptions of  Table  XVII  for  different  bays  and 
spans. 


TABLE  XVIIa.  —  Weight    of   Truss    Skeleton     per    Square 
Foot  of  Area  Covered. 

30-Foot  Span. 


1 

2 

3 

4 

5 

1  • 

7 

Bay  (feet). 

Load 

45°  Slope 
sq.  ft.  (11 

)S.). 

3( 
Loac 

)°  Slope, 
sq.  ft.  (1 

OS.). 

50 

75 

100 

50 

75 

100 

18  
20  

16 
16 

20 
21 

26 
26 

15 
15 

21 
19 

33 
31 

40-Foot  Span. 


18  
20  

25 
24 

30      39 
30      37 

24 
24 

27 
32 

33 
39 

50-Foot  Span. 

18  
20  

36 
33 

42 
42 

52 
56 

31 
31 

36 
38 

45 
45 

60-Foot  Span. 

18 

42 
42 

53 
50 

72 
67 

39 
39 

46 
46 

57 
54 

20  

70-Foot  Span. 

18  

54 
59 

67 
70 

81 
74 

47 
46 

60 
58 

72 
68 

20  

KOOF    TRUSSES. 


245 


DESCRIPTION  OF  TABLE  XVII6. 

This  table,  with  appended  notes,  gives  complete 
designs  of  trusses  of  the  types  shown  for  the 
spans  and  bays  indicated.  The  only  change  from 
Table  XVII  is  that  wider  bays  are  treated.  To 
keep  the  span  of  the  roof  slabs  for  this  type  of 
truss  within  bounds,  two  intermediates  or  rafters 
are  used,  carried  by  purlins,  spanning  from  truss 
to  truss  and  supported  by  purlin  braces,  molded 


CENTER  OF  TRUSS 


0-                <°             ^ 

,,     z 

,,   RAFTER     z 

z 

"  % 

.,          « 

1 

°   \  * 

,,    °- 

M    TRUSS      a 

* 

diagonally  between  the  rafter  bearings  and  the 
adjacent  vertical  panel  point  members.  The  pur- 
lins have  been  kept  the  same  size  as  the  rafters, 
to  give  sufficient  bearing  for  the  braces. 

Whenever  braces  are  longer  than  the  limit 
stated  under  Table  XVI,  they  should  be  cared  for 
as  there  stated.  This  applies  to  all  tables. 


246      HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVII6. 
30-Foot  Span. 


Bay 

(feet). 

Upper  Chord.     Concrete  Sizes. 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

24  
30  

7X14 
7X16 

8X16 
9.5X16 

9X18 
11  X18 

7X14 
7.5X14 

9.5X16 
10X16 

11.5X16 
13.5X16 

40-Foot  Span. 


24  
30  

8X18 
9.5X18 

9X20 
10.5X20 

11.5X22 
12X22 

9X16 
10X16 

12  X  16 
12.5X18 

12.5X2Q 
14X20 

50-Foot  Span. 


24  
30  

10X20 
10.5X22 

10X24 
11.5X24 

12.5X26 
15X28 

11  X16 
12X18 

12X20 
14.5X20 

13.5X22 
15.5X22 

60-Foot  Span. 


24  

10X24 

11X28 

15X30 

12X20 

14X20 

16.5X24 

30  

11.5X24 

13X28 

15.5X30 

13.5X20 

15X24 

17.5X26 

70-Foot  Span. 


24  

11X28 

13.5X30 

14.5X34 

11.5X24 

14.5X26 

17.5X28 

30  

14X28 

14X32 

15X34 

13X24 

17.5X26 

19X28 

Lower  Chord.     Concrete  Sizes. 


30-Foot  Span. 


24  
30  

4.5X12 
6.5X12 

6X12 
8X12 

7.5X12 
9.5X12 

7.5X12 
9.5X12 

8.5X12 
11X12 

11X12 
12X12 

40-Foot  Span. 


24 

7  X16 

8X16 

9  5  X16 

8  X16 

11  X16 

12X16 

30  .. 

7X16 

8.5X16 

10X16 

10X16 

11.5X16 

14.5X16 

ROOF    TRUSSES. 


247 


TABLE  XVII6.  —  Continued. 
50- Foot  Span. 


Bay 

(feet). 

Lower  Chord.     Concrete  Sizes. 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

24  
30  

9X20 
9X20 

10X20 
10.5X20 

11.5X20 
12X20 

10X20 
12X20 

11.5X20 
13.5X20 

14X20 
16.5X20 

60-Foot  Span. 


24  

9X24 

10X24 

11.5X24 

10X24 

13X24 

14X24 

30  

9X24 

10.5X24 

12X24 

12X24 

13.5X24 

16.5X24 

70-Foot  Span. 


24  
30 

10X28 
10X28 

11X28 
11.5X28 

12.5X28 
13X28 

11X28 
13X28 

14X28 
14.5X28 

15X28 
17.5X28 

30-Foot  Span.     Diagonal  Braces. 

24  
30  

4.5X7 
6.5X6 

6X8 
8X7 

7.5X8 
9X8 

6X8 

8X8 

8X9 
9X10 

10X10 
10X11 

40-Foot  Span. 

24 

7X7 
7X8 

8X8 
8.5X9 

9.5X9 
10X11 

8X9 
9X10 

10X10 
11X11 

11X12 
13X13 

30  

50-Foot  Span. 

24 

9X8 
9X9 

10X10 
10X12 

11X12 

12X12 

10X12 
12X12 

11.5X13 
13.5X16 

14X14 
16X16 

30  

60-Foot  Span. 

24 

9X10 
9X12 

10X13 
10X15 

11.5X14 
12X16 

10X16 
12X17 

13X17 
13.5X20 

14X19 
16.5X20 

30  

70- Foot  Span. 


24  
30  

10X11 
10X15 

11X14 
11.5X16 

12.5X16 
13X19 

11X18 
13X21 

14X20 
14.5X24 

15X24 
17.5X24 

248   HANDBOOK  ON  REINFORCED  CONCRETE. 

TABLE  XVIIfc.  —  Continued. 
30-Foot  Span.     Purlin  Braces. 


Bay 

(feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 
0X0 

24  

3X4 

4X4 

5X5 

4X4 

5X6 

30  

4X4 

4X5 

5X5 

4X5 

5X6 

6X7 

40-Foot  Span. 


24  
30  .  . 

4X5 
5X5 

5X6 
6X6 

6X7 
6X8 

5X6 
6X6 

6X8 

7X8 

8X8 
8X9 

50-Foot  Span. 


24  
30  

5X6 
6X6 

7X7 
7X8 

8X8 
8X9 

7X7 
7X8 

8X9 
9X9 

10X10 
10X11 

60-Foot  Span. 


24  
30  

6X7 
7X7 

8X8 
8X9 

9X10 
10X10 

8X8 
8X9 

10X10 
11X11 

11X12 
12X12 

70-Foot  Span. 


24  
30  .  . 

8X8 
9X9 

10X10 
10X11 

10X12        9X10 
11X12      10X10 

11X12 
12X13 

13X14 
14X14 

NOTE.  —  For  reinforcement  sizes  of  upper  and  lower 
chords;  for  sizes  of  purlins  and  intermediates  or  rafters,  see 
Table  XVII,  noting  that  the  24  and  30-foot  bays  here 
correspond  with  the  18  and  20-foot  bays  there,  respectively. 
For  truss  rod  and  panel  point  rod,  sizes  for  24  and  30-foot 
bays  for  this  table,  refer  to  Table  XVII,  and  increase  the 
values  given  for  18  and  20-foot  bays  for  like  spans,  respec- 
tively, by  one-third  in  the  first  case,  and  one-half  in  the 
second. 


ROOF   TRUSSES. 


249 


24-30  FT,  BAYS 

CURVES  SHOWING  TH'E  RELATION 
OF  COST  TO  SPAN 

(For  Type  of  Truss  see  Table  17-2) 


( 

4U- 

x 

c 

X 

o 

X* 

X 

0) 

|X 

x 

/ 

^ 

x^ 

</5 

X1 

x 

^ 

x- 

< 

<v 

X" 

x 

x^ 

x' 

x 

CO 

?\ 

^ 

^ 

X 

^ 

x-- 

la 

^ 

x* 

' 

? 

x. 

r^ 

O 

10 

j; 

? 

^ 

ix' 

t 

,  • 

^ 

I 

i 

X* 

t 

+1 

n 

<D 

,x 

! 

**"! 

c 

^ 

X 

^ 

cr 

• 

^ 

^ 

fe! 

*-- 

10  » 

>» 

Q. 

c 

crt 

/ 

C 

ft.  in 

^ 

X 

n  o 

04U 

x> 

C/) 

^ 

X 

tT> 

X 

x 

X 

to 

•<J- 

X 

X 

0 

/ 

' 

/ 

O 

ll 

/ 

X 

X 

f\ 

^ 

X" 

^ 

X 

4! 

9) 

*> 

J 

/ 

^x 

?V 

X 

, 

i 

X 

X 

cr 

^ 

^ 

/ 

,v 

X 

^ 

v)  20 

N0^ 

/ 

', 

k 

^ 

I  x 

X 

V 

, 

/ 

/ 

X" 

CL 

S1 

^ 

3 

s 

S 

> 

' 

c 

en 

^ 

0  IU 

5 

.— 

00 

o  o 

3 

0 

4 

0 

5 

0 

6 

0 

7 

0 

Span  in  Feet 


250      HANDBOOK   ON    REINFORCED   CONCRETE. 


TABLE  XVII&!.  —  Weight  of  Truss  Skeleton  per  Square  Foot 

of  Area  Covered 

30-Foot  Span 


1 

2 

3 

4 

5 

6 

7 

Bay 

(feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

38 
33 

24 

19 

18 

23 

24 

31 
30 

18 
17 

25 

22 

30  

40-Foot  Span. 


24  

29 

27 

36 
34 

45 
40 

28 
27 

31 
35 

37 

42 

30 

50-Foot  Span. 

24  

41 
51 

48 
46 

60 
62 

35 
34 

42 
42 

53 
49 

30  

60-Foot  Span. 

24 

48 
46 

61 
56 

82 
74 

45 
43 

53 

51 

65 
60 

30  

70-Foot  Span. 

24  

62 
65 

76 
63 

93 

81 

53 

51 

68 
59 

82 
74 

30  

ROOF   TRUSSES. 


251 


DESCRIPTION  OF  TABLE  XVIIc. 

Table  XVIIc,  with  notes,  treats  the  design  of 
truss  here  shown  for  the  same  bays  as  Tables  XVII 
and  XVII6,  using  similar  construction  details  as 


CENTER  OF  TRUSS 


SPAN •} 


there  stated.  The  only  change  has  been  the  add- 
ing of  two  more  panel  points,  thereby  obtaining 
satisfactory  designs  for  longer  spans. 

TABLE  XVIIc. 

45-Foot  Span. 


Upper  Chord.     Concrete  Sizes. 


1 

2 

3 

4 

•    1 

6 

7 

Bay 

(feet). 

Load  i 

45°    Slope 
>er  sq.  ft. 

(Ibs.). 

Load  ] 

30°    Slop( 
aer  sq.  ft. 

& 

"(Ibs.). 

50 

75 

100 

50 

75 

100 

18  
20  

7X14 
7X16 

8.5X16 
9  5  X16 

9.5X18 
11  X18 

7.5X14 
7  5  X14 

10X16 
10X16 

12.5X16 
13X16 

24 

8  5X14 

9  X16 

11  X18 

9  X14 

12X16 

14  5X16 

30      . 

8  5X16 

11  5X16 

12  5  X18 

9  5  X16 

12  5X16 

17  5X16 

NOTE.  —  For  sizes  of  purlins,  intermediates,  purlin  braces, 
diagonal  braces,  truss  and  panel  point  rods,  and  reinforce- 
ment sizes  for  upper  and  lower  chords,  see  Table  XVII, 
span  30  feet,  and  corresponding  bays. 


252 


HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVIIc.  —  Continued. 
60-Foot  Span. 


1 

Upper  Chord.     Concrete  Sizes. 

2 

3 

* 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

18  
20  

8X18 
9.5X18 
9.5X18 
11.5X18 

9.5X20 
10.5X20 
11X20 
12.5X20 

12X22 
12X22 
14.5X22 
15X22 

9.5X16 
10X16 
11.5X16 
13X16 

12.5X16 
12.5X18 
16.5X16 
16.5X18 

13.5X20 
14X20 
16.5X20 
18.5X20 

24 

30  

NOTE.  —  Corresponds  with  Table  XVII,  40-foot  span,  for 
all  sizes  not  given  here. 

75-Foot  Span. 


18       
20 

10.5X20 
10.5X22 
12X20 
13X22 

10.5X24 
11.5X24 
12X24 
13X24 

13X26 
14.5X28 
15.5X26 
19X28 

11.5X16 
11.5X18 
14X16 
15.5X18 

12.5X20 
14.5X20 
15.5X20 
18X20 

15.5X22 
16.5X22 
17.5X22 
20.5X22 

24 

30       

NOTE.  —  Corresponds  with  50-foot  span,  Table  XVII,  for 
all  sizes  not  given  here. 

90-Foot  Span. 


18  
20  

10.5X24 
11.5X24 
12X24 
14X24 

11.5X28 
13X28 
13X28 
16X28 

15.5X30 
15.5X30 
19.5X30 
20X30 

13X20 
13.5X20 
15X20 
18X20 

15X20 
15X24 
18X20 
19.5X24 

17.5X24 
17.5X26 
21.5X24 
22.5X26 

24 

30  

105-Foot  Span. 


18  
20  .... 

11.5X28 
14X28 
13X28 
17X28 

14X30 
14X32 
17X30 
17X32 

15X34 
15X34 
18X34 
18X34 

12X24 
13X24 
15X24 
16.5X24 

16X26 
17.5X26 
19X26 
22.5X26 

18.5X28 
20X28 
23X28 
26X28 

24  

30  .. 

NOTE.  —  For  weight  per  square  foot  of  projected  area 
covered  see  Tables  XVII  and  XVII&,  and  add  about  10 
per  cent. 


ROOF   TRUSSES. 

TABLE  XVIIc.  —  Continued. 
45-Foot  Span. 


253 


Bay 

(feet). 

Lower  Chord.     Concrete  Sizes. 

8 

9 

10 

11 

12 

13 

45°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  per  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

11.5X12 
11.5X12 
15X12 
17X12 

18 

5X12 
6X12 
7X12 
8.5X12 

6X12 
7X12 
8X12 
11.5X12 

7X12 
9X12 
10X12 
13X12 

7X12 
9X12 
10X12 
13X12 

9X12 
11X12 
11.5X12 
15X12 

20       .    . 

24  
30 

60-Foot  Span. 


18 

7  X16 

8  5  X16 

10  X16 

8  5  X16 

11  5X16 

13  X16 

20  
24 

7X16 
8  5  X16 

8.5X16 
10  X16 

10X16 
12  5  X16 

10X16 
10  X16 

11.5X16 
14  5  X16 

14.5X16 
16  X16 

30  

8.5X16 

10.5X16 

13X16 

13X16 

15.5X16 

19.5X16 

75- Foot  Span. 


18  

9X20 
9X20 
10.5X20 
10.5X20 

10.5X20 
10.5X20 
12X20 
12.5X20 

12X20 
12X20 
14.5X20 
15X20 

10.5X20 
12X20 
12X20 
15X20 

12X20 
13.5X20 
14.5X20 
17.5X20 

15X20 
16.5X20 
18»X20 
21.5X20 

20 

24  
30  .. 

90-Foot  Span. 


18  
20 

9X24 
9X24 

10.5X24 
10.5X24 

12X24 
12X24 

10.5X24 
12X24 

13.5X24 
13  5  X24 

15X24 
16  5X24 

24  
30  

10.5X24 
10.5X24 

12X24 
12.5X24 

14.5X24 
15X24 

12X24 
15X24 

16.5X24 
17.5X24 

18X24 
21.5X24 

105-Foot  Span. 


18 

10  X28 

11.5X28 

13X28 

11  5X28 

14  5X28 

16  X2S 

20  

10X28 

11.5X28 

13X28 

13X28 

14.5X28 

17.5X28 

24  

11.5X28 

13X28 

15.5X28 

13X28 

17.5X28 

19X28 

30  

11.5X28 

13.5X28 

16X28 

16X28 

18.5X28 

22.5X28 

254      HANDBOOK   ON    REINFORCED   CONCRETE. 


DESCRIPTION  OF  TABLE  XVIId 

This  table,  with  notes,  contains  data  for  design- 
ing trusses  of  the  class  shown.     The  only  change 


over  Table  XVIIc  is  that  longer  spans  have  been 
treated  by  using  eight  panels. 


TABLE  XVIW. 
60-Foot  Span. 


Sizes  of  Upper  Chord. 


Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

9X14 
f  X14 
11X14 
12X14 

75 

100 

18  
20  

8X14 
8X16 
10X14 
10X16 

10X16 
11X16 
13X16 
14X16 

11X16 

13X18 
13X18 
14X18 

12X16 
12X16 
15X16 
16X16 

15X16 
16X16 
18X16 
22X16 

24  
30  

80-Foot  Span. 


18  

9X18 

11X20 

14X22 

11  X16 

15X16 

16X20 

20  

11X18 

12X20 

14X22 

12X16 

15X18 

17X20 

24 

12X18 

13X20 

17  X22 

14  X16 

19X16 

20X20 

30  

14X18 

13X20 

18X22 

16X16 

20X18 

23X20 

ROOF  TRUSSES. 


255 


TABLE  XVIId.  —  Continued. 
100-Foot  Span. 


Bay  (feet). 

Sizes  of  Upper  Chord. 

45  Slope. 
Load  sq.  ft.  (Ibs.). 

30  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

18  
20  
24 

12X20 
12X22 
14X20 
15X22 

12X24 
13X24 
14X24 
16X24 

15X26 
17X28 
18X26 
23X28 

14X16 
14X18 
18X16 
19X18 

15X20 

17X20 
19X20 
23X20 

19X22 

20X22 
21X22 
25X22 

30  

120-Foot  Span. 


18 

12  X24 

13  X28 

18X30 

15  X20 

18  X20 

14  X24 

20  
24  

13X24 
14X24 

15X28 
15X28 

18X30 
23X30 

16X20 
18X20 

18X24 
22X20 

21X26 
24X24 

30  .. 

16X24 

19X28 

23X30 

21X20 

24X24 

28X26 

140-Foot  Span. 


18  

13X28 

16X30 

17X34 

14X24 

18X26 

22X28 

20  

14X28 

16X32 

17X34 

15X24 

21X26 

23X28 

24  

15X28 

19X30 

20X34 

17X24 

22X26 

25X28 

30  

20X28 

20X32 

21X34 

20X24 

28X26 

30X28 

60-Foot  Span. 


Sizes  of  Lower  Chord. 


Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

18  

5.5X12 
7.5X12 
6.5X12 
10.5X12 

7.5X12 
9.5X12 
9.5X12 
13.5X12 

9.5X12 
11.5X12 
12.5X12 
16.5X12 

9.5X12 
11.5X12 
12.5X12 
16.5X12 

11.5X12 
13.5X12 
14.5X12 
19.5X12 

15.5X12 
15.5X12 
19.5X12 
21.5X12 

20 

24  
30  

80- Foot  Span. 


18  

8X16 

10X16 

12  X16 

10  X16 

14X16 

16  X16 

20 

8  X16 

10  X16 

12  X16 

12  X16 

14  X16 

18  X16 

24  

10X16 

12X16 

15X16 

12X16 

18X16 

20X16 

30  

10X16 

12X16 

16X16 

16X16 

19X16 

25X16 

256       HANDBOOK   ON    REINFORCED    CONCRETED 


TABLE  XVIId  —  Continued. 
100-Foot  Span. 


Bay  ffeet). 

Sizes  of  Lower  Chord. 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

14X20 
16X20 
17X20 
21X20 

100 

18  

10X20 
10  X20 
12X20 
12X20 

12X20 
12X20 
14X20 
15X20 

14X20 
14X20 
17X20 
18X20 

12X20 
14X20 
14X20 
18X20 

18X20 
20X20 
22X20 
27X20 

20 

24  
30  .. 

120-Foot  Span. 


18  
20  

10X24 
10X24 

12X24 
12X24 

14X24 
14X24 

12X24 
14X24 

16X24 
16X24 

18X24 
20X24 

24 

12X24 

14X24 

17X24 

14X24 

20X24 

22X24 

30  

12X24 

15X24 

18X24 

18X24 

21X24 

27X24 

140-Foot  Span. 


18 

11  X28 

13X28 

15  X28 

13X28 

17X28 

19X28 

20  
24 

11  X28 
13X28 

13X28 
15  X28 

15X28 
18X28 

15X28 
15X28 

17X28 
21X28 

21X28 
23X28 

30  

13X28 

16X28 

19X28 

19X28 

22X28 

28X28 

NOTE.  —  For  all  sizes  not  given  here,  refer  to  Tables  XVII 
and  XVII6  to  corresponding  bays,  bearing  in  mind  the 
following  change  in  spans: 

A  60-foot  span  here  corresponds  with  30-foot  span  under 
Tables  XVII  and  XVII6. 

A  80-foot  span  here  corresponds  with  40-foot  span  under 
Tables  XVII  and  XVII6. 

A  100-foot  span  here  corresponds  with  50-foot  span  under 
Tables  XVII  and  XVII6. 

A  120-foot  span  here  corresponds  with  60-foot  span  under 
Tables  XVII  and  XVII6. 

A  140-foot  span  here  corresponds  with  70-foot  span  under 
Tables  XVII  and  XVII6. 

For  weight  per  square  foot  of  projected  area  covered,  see 
Tables  XVII  and  XVIIfe,  and  add  about  20  per  cent.  Ref- 
erence spans  under  Tables  XVII  and  XVII6  are  one-half 
those  given  here  for  obtaining  corresponding  weights. 


ROOF  TRUSSES.  257 

GENERAL    DESCRIPTION    OF   TYPES    OF   TRUSSES 

"XVII  TO  XVIId." 

The  upper  chord  in  Tables  XVII  to  XVIM 
have  been  figured  for  a  uniform  section  through- 
out their  length,  and  of  a  section  to  withstand  the 
stress  at  the  most  stressed  part,  namely  at  the 
center  between  either  of  the  two  bearings  and  the 
first  panel  point  from  either  bearing.  In  cases 
where  the  conditions  will  allow,  it  is  very  econom- 
ical to  vary  the  section,  either  by  tapering  the 
width  uniformly  from  the  bearings  to  the  apex, 
called  "condition  A,"  or  by  forming  steps  at  each 
panel  point,  termed  "  condition  B."  The  sizes  were 
figured  with  this  in  view,  as  it  may  be  noted  that 
the  depths  are  such  as  to  withstand  the  bending 
moment  due  to  the  distributed  loads  for  econom- 
ical widths  and,  to  care  for  concentrated  loads, 
these  widths  were  increased,  keeping  the  same 
depths  as  previously  determined.  If  condition  B 
is  adopted,  the  sizes  of  sections  in  the  different 
panels  for  the  tables  specified  will  be  as  follows: 
TABLES  XVII  AND  XVII6. 


Panel. 


Concrete  Sizes. 


First  from  apex. . 


Table  17-c. 

First  from  apex. . . 

Second  from  apex. 
Table  17-rf. 

First  from  apex... 

Second  from  apex. 

Third  from  apex. . 


Reinforcement  size  +  f  the  difference  between 
the  reinforcement  sec- 
tion and  the  concrete 
section  given  for  upper 
chords.  Call  this  dif- 


ference x. 


Reinforcement  size'+  £  x. 
Reinforcement  size  +  |  x. 

Reinforcement  size  +  f  x.. 
Reinforcement  size  +  f  x. 
Reinforcement  size  +  5  x. 


258      HANDBOOK  ON   REINFORCED    CONCRETE. 

If  condition  A  is  adopted,  sizes  corresponding 
with  the  above  should  be  used  at  the  center  of 
the  different  panels. 

DESCRIPTION  OF  TABLE  XVIII. 

This  table  covers  the  complete  design  of  a  dif- 
ferent class  of  truss,  shown  by  the  sketch.  In 
the  design  the  purlins  are  kept  near  enough  to- 
gether to  carry  the  roof  slabs.  Two  spacings  of 
purlins  have  been  used,  namely  8-foot  and  10-foot. 
The  span  headings  of  each  set  of  bays  clearly 
state  which  of  the  two  panelings  to  use,  or  has 
been  used. 


CENTER  OF  TRUSS 


t 

1 

OH  WALL 
•-BAY  

PURLIN 

PURLIN 

-            ~ 

PURLIN 

1 

c 

ENTER 

DF  TRUrSS 

HALF  PLAN  PLAN  HALF  ^^ 

18  <&  ZO  FT.  BAYS  24  A  30  FT.  BAYS 


TYPE   18 


The  table,  as  drawn  up,  has  limited  the  purlin 
span  or  the  bay  to  24  feet.  It  will  be  readily 
seen  that  this  may  be  increased,  using  the  same 
sizes  of  purlins*  required  for  the  bays  given,  by 
molding  in  braces  diagonally  between  the  purlins 
and  the  adjacent  vertical  tie  members,  so  as  to 


ROOF   TRUSSES.  259 

limit  the  purlin  span  proper  to  the  values  used  in 
the  table. 

Under  "Diagonal  Braces"  it  is  noted  that  the 
sizes  given  are  for  the  worst  cases.  Such  cases, 
as  may  be  seen,  occur  at  the  first  panel  point  from 
the  bearings  where  the  braces  make  angles  of  60 
degrees  when  a  30-  degree  slope  of  truss  is  used, 
and  45  degrees  when  a  45-  degree  slope  truss  is 
used,  with  vertical  through  the  panel  points  in 
question.  Accordingly,  the  sizes  of  the  other 
diagonals  may  be  reduced  in  accordance  with  the 
relation  that  the  sines  of  the  angles  between  ver- 
ticals through  such  panel  points  and  their  cor- 
responding braces  bear  to  the  sine  of  60  degrees 
for  a  30-degree  slope  truss,  and  to  the  sine  of  45 
degrees  for  a  45-degree  slope  truss. 

Again,  it  may  be  discovered  that  the  sizes 
figured  are  for  10-foot  panels.  If  8-foot  panels 
are  used  instead,  the  values  given  may  again  be 
reduced  20  per  cent.  If  the  first  reduction  is 
adhered  to,  particular  attention  should  be  paid 
to  excessively  long,  unsupported  lengths,  and 
the  effect  of  eccentricity  thereon  as  previously 
treated. 

This  type  of  truss  may  be  tapered  uniformly, 
or  offset  in  width  over  panel  points  as  stated  in 
the  general  description  for  Tables  XVII  to 
XVlId. 


260      HANDBOOK   ON   REINFORCED   CONCRETE. 

GENERAL  DESCRIPTION  OF  "  XVIII"  TYPE  TRUSS. 

In  designing  trusses  of  this  type,  the  following 

formula   is   submitted   in   determining   the   total 

stress  in  pounds  in  any  part  or  panel  of  the  upper 

chord. 

Let    k  =  a  factor  to  be  determined  from  the 

following  plot. 
6  =  bay  in  feet, 
s  =  span  in  feet. 
w  =  total  load  per  square  foot  including 

weight  of  roof  proper. 
n  =  total  number  of  panels  into  which  the 

span  is  divided,  either  8  or  10  feet. 
W  =  total  stress  in  pounds  in  any  panel. 
For  45-degree  slope : 
1st.    Panel  from  apex,TF  equals  1.5  (k'b-s-w)  x  1.42. 

2d.     Panel  from  apex,F  equals  2.5  (k'b'8-w)  x  1.42. 
3d.     Panel  from  apex,TF  equals  3.5  3^Sl  X  1.42. 

4th.  Panel  from  apex,F  equals  4.5  (k-b's'w)  x  1.42. 

etc. 

For  30  degree  slope  use  factor  2.0  instead  of 
1.42  as  given  for  45  degree  slope. 

The  above  stress  divided  by  500  will  give  the 
area  of  concrete  section  required  for  concentrated 
loading  in  addition  to  the  section  which  has  to 
care  for  the  distributed  loading  and  which  equals 
the  section  so  called  "  Reinforcement  Size  in  Table 
XVIII." 


ROOF   TRUSSES. 


261 


1.90 


TABLE  18 

PLOTTO  DETERMINE  VALUES  FOR 
FACTOR  "K"  IN  FORMULA. 


1.80 


1.70 


1.60 


1.50 


1.40 


1.30 


1.20 


1.10 


246  8  10  1.2 

Total  Number  of  Panels. 


262      HANDBOOK    ON    REINFORCED    CONCRETE. 

To  determine  the  size  of  lower  chord  correspond- 
ing to  any  upper  chord  to  care  for  concentrated 
loading,  reduce  the  concrete  section  of  the  upper 
chord  for  concentrated  loading  by  29.5  per  cent 
for  45  degree  slopes,  and  by  13.5  per  cent  for  30 
degree  slopes.  In  addition  to  this  section,  increase 
the  size  by  the  section  required  to  support  this 
distributed  load  over  a  length  equal  to  the  panel, 
as  stated  earlier  in  the  description. 


TABLE  XVIII. 
30-Foot  Span  (8-Foot  Panels). 


1 

Upper  Chord.      Concrete  Sizes. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14 

6.5X16 
6.5X18 
7.5X20 
8X22 
8X24 
9X24 

7X20 
8.5X20 
8.5X22 
9.5X24 
9.5X26 
10.5X28 

8.5X20 
8.5X24 
10X24 
10X28 
11X28 
11X32 

7X16 
7X18 
8X20 
8.5X22 
8.5X24 
9.5X24 

7.5X20 
9X20 
9X22 
10X24 
10X26 
11X28 

9.5X20 
9.5X24 
10.5X24 
10.5X28 
12X28 
12X32 

16  
18  
20  

22 

24  .  . 

40- Foot  Span  (10-Foot  Panels). 


14 

7X18 
7X20 
8X22 
8X24 
9X24 
9X28 

8.5X20 
8.5X22 
9.5X24 
9.5X28 
10.5X28 
10.5X30 

9X22 
10X24 
10X26 
11X28 
11X32 
12X32 

7.5X18 
7.5X20 
8.5X20 
8.5X24 
9.5X24 
9.5X28 

9.5X20 
9.5X22 
10.5X22 
11X26 
11.5X28 
11.5X30 

10X24 
11X22 
11X26 
12.5X28 
12.5X32 
13.5X32 

16  
18  

20  
22       

24  

ROOF    TRUSSES. 


263 


TABLE  XVIII.  —  Continued. 
50-Foot  Span  (8-Foot  Panels.) 


1 

Upper  Chord.     Concrete  Sizes. 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14  
16  
18  
20  
22 

7.5X16 
7.5X18 
8.5X20 
9X22 
9X24 
10X24 

8X20 
9.5X20 
9.5X22 
10.5X24 
11X26 
12X28 

10X20 
10X24 
11.5X24 
11.5X28 
12.5X28 
12.5X32 

8.5X16 
8.5X18 
9.5X20 
10X22 
10X24 
11X24 

9.5X20 
11X20 
11X22 
12X24 
12X26 
13X28 

11.5X20 
11.5X24 
13X24 
13X28 
14X28 
14.5X32 

24  

60-Foot  Span  (10-Foot  Panels). 


14 

8X18 

10X20 

10.5X32 

9X18 

11.5X20 

12.5X22 

16  
18 

8X20 
9X22 

11X20 
11  X22 

11.5X24 
12X26 

9X20 
10X22 

11.5X22 
13X24 

14X24 
14X26 

20  
22  
24  

9X24 
10.5X24 
11.5X24 

11X24 
12.5X26 
12.5X28 

13X28 
13X32 
14.5X32 

10.5X24 
11.5X24 
11.5X28 

13X26 
14X28 
14X30 

15X28 
15X32 
16.5X32 

80-Foot  Span  (10-Foot  Panels). 


14  

8X18 

11.5X20 

12.5X22 

10.5X18 

13.5X20 

15X22 

16  

9X20 

11.5X22 

14X24 

10.5X20 

14X22 

16X24 

18  

10X22 

12.5X24 

14X26 

12X22 

15X24 

17X26 

20 

10  5X24 

13X26 

14X28 

12X24 

15X26 

18X28 

22  

11.5X24 

14X28 

15X32 

13.5X24 

16X28 

18X32 

24  

11.5X28 

14X30 

16.5X32 

13X28 

16.5X30 

19.5X32 

100  Foot  Span  (10  Foot  Panels). 


14           .... 

10X18 

13X20 

14.5X22 

12X18 

16X20 

17.5X22 

16 

10X20 

13X22 

15.5X24 

12.5X20 

16X22 

15X24 

18               .    . 

11.5X22 

14.5X24 

16X26 

14X22 

17X24 

20X26 

20  
22 

11.5X24 
13X24 

14.5X26 
16X28 

17X28 
17X32 

14X24 
15.5X24 

17.5X26 
19X28 

21X28 
21X32 

24  

13X28 

16X30 

19X32 

15.5X28 

19X32 

23X32 

264       HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVIII.  —  Continued. 
30-Foot  Span  (8-Foot  Panels). 


Bay  (feet). 

Lower  Chord.     Concrete  Sizes. 

8 

9 

10 

11 

12 

13 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14  

4.5X8 
5X8 
4.5X10 
5X10 
5X10 
5X12 

5X10 
5X12 
5.5X12 
6X12 
6.5X12 
6.5X12 

5.5X12 
6X12 
6X12 
6.5X12 
7X12 
7.5X12 

5.5X10 
6X10 
5.5X12 
6X12 
6.5X12 
7X12 

6X12 
6.5X12 
6X14 
6.5X14 
7X14 
7X16 

6.5X14 
7.5X14 
8X14 
8X16 
8.5X16 
9X16 

16  
18  
20  

22  
24  

40-Foot  Span  (10- Foot  Panels). 


14 

4  5X10 

5  5X12 

6  X12 

5  5X12 

6  X14 

8X16 

16  
18 

5X10 
5  5X10 

6X12 
6  5X12 

6.5X12 
7  X12 

6X12 
6  5X12 

6.5X14 

7  X14 

8X16 
8  5  X16 

20  
22  
24  .  . 

5X12 
5.5X12 
6X12 

6.5X12 
7X12 
7X12 

7.5X12 
7X14 
7.5X14 

7X12 
6X14 
6.5X14 

7X16 
8X16 
8.5X16 

9X16 
9.5X16 
10  X16 

50- Foot  Span  (8-Foot  Panels). 


14  

5X12 

6X12 

7X12 

6.5X12 

8X14 

8.5X16 

16  

5.5X12 

6.5X12 

7X14 

6X14 

8X16 

9.5X16 

18  

6X12 

7X12 

7.5X14 

6.5X14 

8.5X16 

10X16 

20  

6  5X12 

7  5X12 

7  5X16 

7X14 

9X16 

10X18 

22  

6.5X12 

7X14 

8X16 

7X16 

9.5X16 

10.5X18 

24  .. 

7X12 

7.5X14 

8.5X16 

8X16 

10X16 

10.5X20 

ROOF    TRUSSES. 


265 


TABLE  XVIII.  —  Continued. 
60-Foot  Span  (10-Foot  Panels). 


Bay  (feet). 

Upper  Chord.     Concrete  Sizes. 

8 

9 

10 

11 

12 

13 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14  
16  

6.5X12 
6.5X12 
7X12 
7X12 
7X12 
7.5X12 

7X12 
7.5X12 
7X14 
7.5X14 
7.5X16 
8X16 

7.5X14 
7.5X16 
8X16 
8.5X16 
8.5X18 
9.5X18 

6.5X14 
7X14 
7X16 
8X16 
8.5X16 
9X16 

8.5X16 
9X16 
9.5X16 
10X16 
10X18 
10.5X18 

10X16 
10X18 
10.5X18 
10.5X20 
10.5X22 
11  X24 

18  
20  
22 

24  

80- Foot  Span  (10-Foot  Panels). 


14  

6X14 

7.5X14 

8X16 

8X16 

8X20 

8X2G 

16  

6.5X14 

8X16 

8X18 

8.5X16 

8X22 

8.5x:s 

18  

7X14 

8.5X16 

8X20 

8X18 

8X24 

9XCO 

20  

7.5X14 

8X18 

8X22 

8X20 

8X26 

10X30 

22  

7X16 

8.5X18 

8X24 

8.5X20 

8X28 

11X30 

24  

7.5X16 

9X18 

8X26 

8X22 

8X30 

12X30 

100-Foot  Span  (10-Foot  Panels). 


14  
16 

7X14 
7  5X16 

8.5X16 
8X18 

8X20 
8X22 

8X18 
8X20 

8X24 
8X26 

9X30 
10X30 

18  
20  

8X16 
8.5X16 

8X20 
8X22 

8X26 
8X28 

8X22 
8X24 

8X30 
10X30 

12X30 
13X30 

22  
24  

8X18 
8X18 

8X24 
8X26 

8.5X28 
9X28 

8X26 
8.5X26 

11X30 
12X30 

14X30 
15X30 

266 


HANDBOOK    ON    REINFORCED    CONCRETE. 


TABLE  XVIII.  —  Continued. 
Reinforcement  Sizes  for  Upper  Chord. 


8-Foot  Panels. 

10-Foot  Panels. 

Bay  (feet). 

Load  sq.  ft.  (Ibs.) 

Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14  

5X16 

5X20 

6X20 

5X18 

6X20 

6X22 

16  

5X18 

6X20 

6X24 

5X20 

6X22 

7X24 

18  

6X20 

6X22 

7X24 

6X22 

7X24 

7X26 

20  

6X22 

7X24 

7X28 

6X24 

7X26 

8X28 

22  

6X24 

7X26 

8X28 

7X24 

8X28 

8X32 

24  

7X24 

8X28 

8X32 

7X28 

8X30 

9X32 

Diagonal  Braces  (Figured  for  Worst  Case).     Sizes  in  Sq.  In. 


14  
16  

45°  Slope  (10-Foot  Panels). 

30°  Slope  (10-Foot  Panels). 

1 
15 
17 
19 
21 
23 

20 
23 
26 
29 
32 
35 

26 
30 
34 
38 
42 
46 

19 
21.5 
24 
26.5 
29.0 
31.5 

28 
32 
36 
40 
44 
48 

38 
43 
48 
53 
58 
63 

18 

20  
22  

24  

Truss  Rod  Sizes  at  Panel  Points.     (Sq.  In.) 

14  
16  
18  
20 

8-Foot  Panels. 

10-Foot  Panels. 

.56 
.64 

.72 
.80 
.88 
.96 

.84 
.96 
1.08 
1.20 
1.32 
1.44 

1.12 
1.28 
1.44 
1.60 
1.76 
1.92 

.70 
.80 
.90 
1.00 
1.10 
1.20 

1.05 
1.20 
1.35 
1.50 
1.65 
1.80 

1.40 
1.60 
1.80 
2.00 
2.20 
2.40 

22       .... 

24  

For  truss  rod  sizes  at  apex,  double  the  values  given  above. 


ROOF   TRUSSES. 


267 


EXPLANATORY  NOTE. 

For  the  sizes  of  purlins  and  reinforcement  for 
this  type  of  truss,  see  Table  II,  Part  III,  for  the 
corresponding  spans  and  loading. 

AVERAGE  OF  BAYS  14-24  FT. 

CURVES  SHOWING  THE  RELATION 

OF  COST  TO  SPAN 

(For  Type  of  Truss  see  Table  18)  x-s 


30 


20 


10 


o 

Ll_ 
10  ^ 

6- 

<u 
0  Q. 

CO 

c 
(U 

o 

c 


40  50  €0 

Span  in  Feet 


80 


100 


For  the  reinforcement  sizes  of  the  lower  chord 
first  determine  the  total  weight  between  panel 
points  of  the  concrete  sizes  here  given,  and  then 
by  reference  to  Table  II,  Part  III,  the  sizes  of 


268      HANDBOOK    ON    REINFORCED    CONCRETE. 


(AVERAGE  BAY  14  FT.) 

CURVES  SHOWING  COMPARATIVE  COSTS 

OF  DIFFERENT  KINDS  OF  TRUSSES 

Full  lines  represent  truss  shown  in  Table  16 
Broken"        "  "          "      "      "     18 


30 


40  50  60  70 

Span  in  Feet 


ROOF   TRUSSES. 


269 


AVERAGE  BAY  20  FEET, 

CURVES  SHOWING  COMPARATIVE  COSTS 

OF  DIFFERENT  KINDS  OF  TRUSSES. 

Full  lines  represent  truss  shown  in  Table  17 
Broken  »         "  "          <<      »      "     i8 


X 

^-^ 

*~* 

^ 

^ 

f 

0 

-  r\9S 

Q   IS 

ji. 

1  — 

a> 

o1^. 

nO     ^S" 

u-     *  "^ 

Q 

1 

t^°     x^ 

x  •  f**  ** 

o 

•i  <;n  " 

^  "r 

** 

*  ' 

o    50  I 

i 

er 

:J 

;2^* 

20  o 

m 

**'*<*'* 

X 

i 

$ 

J09 

DRE)—  ^  = 

t- 

^4.n 

^ 

w 

-50^^ 

Q.-cj,_j32-  - 

e-=    " 

10  ^ 

42     : 

6°  v 

? 

**- 

^ 

c- 

Q 

? 

c  30  - 

-  -  -5 

>  ^ 

0   S 

^^  x 

-^ 

«JU  x 

,  op£ 

|  , 

.   —  ' 

1 

8" 

0) 

w  on    _ 

Q.  iX         LnS. 

o 

y/ 

^•&*  tf 

-  x    S  2  ?  ! 

c 

^ 

^ 

0  P;  £  - 

'   *    2l 

(45! 

S    f   >b 

.  — 

trt 

--=* 

fl''\ 

5(    UBS 

o 

10- 

T' 

^J  — 

m    —  -- 

30  40  50  60  70  80  90  100 

Span  in  Feet. 


270      HANDBOOK   ON    REINFORCED   CONCRETE. 


beams  to  carry  these  distributed  loads  for  the 
required  spans  may  be  found.  Again,  by  referring 
this  latter  size  to  Table  I,  Part  III,  the  required 
reinforcement  may  be  found. 

TABLE   XVIIIa.—  Weight  of    Truss  Skeleton  per  sq.   ft.    of- 
Area  Covered. 

30-Foot  Span  (8-Foot  Panels). 


1 

2    |    3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14  
16  
18  

14 
14 
15.5 
16.5 
16.5 
17. 

19.5 
20.5 
20.5 
21.8 
21.3 
22.5 

24 
25 
25.5 
26.3 
26.4 
28.5 

14.3 
14.2 
15.2 
15.6 
15.5 
15.7 

18.5 
19.6 
19.2 
20.1 
20.0 
21.4 

24.4 
24.5 
25. 

25.7 
26.3 
27.2 

20 

22  
24  

Average 

15.6 

20.9 

25.9 

15.1 

19.8 

26.6 

40-Foot  Span  (10-Foot  Panels). 


14  

17.6 

24.5 

28.3 

17.7 

23.8 

28.8 

16  

17.2 

23.4 

29.1 

16.9 

23.0 

30.0 

18  

18.4 

24.5 

28.2 

16.6 

22.3 

28.6 

20  

18.3 

25.8 

27.7 

18.5 

24.3 

30.5 

22  

18.6 

25.1 

30.2 

17.3 

24.9 

29.9 

24  

19.5 

24.4 

30.2 

18.6 

24.6 

30.5 

Average 

18.3 

24.6 

28.9 

17.4 

23.8 

29.7 

50- Foot  Span  (8- Foot  Panels). 


14  

18.3 

25.1 

29.9 

18.2 

26.0 

31.6 

16  

18.1 

25.2 

31.0 

18.3 

26.3 

32.6 

18 

19  4 

25  0 

31  3 

19  0 

25  6 

32  0 

20  

19.9 

26.4 

32.6 

19.3 

26.2 

33.1 

22  

19.4 

26.7 

32.4 

19.4 

24.9 

32.2 

24  

19.7 

27.2 

33.4 

19.8 

26.6 

34.3 

Average 

19.1 

26.1 

31.7 

19.0 

25.9 

32.6 

ROOF  TRUSSES. 


271 


TABLE  XVIIIa.  —  Continued. 
60- Foot  Span  (10-Foot  Panels). 


1 

2 

3 

4 

5 

6 

7 

Bay  (feet). 

45°  Slope. 
Load  sq.  ft.  (Ibs.). 

30°  Slope. 
Load  sq.  ft.  (Ibs.). 

50 

75 

100 

50 

75 

100 

14  

22.7 
21.6 
22.8 
22.1 
22.9 
23.6 

30.2 
28.8 
30.0 
29.3 
32.0 
31.0 

35.9 
36.7 
36.4 
37.5 
38.8 
39.4 

22.4 
21.2 
22.9 
23.4 
23.0 
23.8 

32.2 
30.9 
31.6 
30.7 
31.9 
31.1 

38.7 
39.5 
37.9 
38.8 
39.8 
40.0 

16  

18  
20 

22  
24 

Average 

22.6 

30.2 

37.5 

22.8 

31.4 

39.1 

80-Foot  Span  (10-Foot  Panels). 


14  
16 

24.0 
24  9 

35.0 
35  9 

43.5 
45  3 

27.3 

26  8 

38.0 
37  3 

47.4 
48  0 

18  
20  
22 

26.1 
26.7 
26  1 

36.7 
36.1 
37  0 

44.0 
42.5 
46  0 

27.8 
27.4 
28  4 

38.0 
37.0 
38  0 

48.7 
49.5 
50  7 

24  

27.4 

36.5 

46.5 

27.6 

37.9 

50.5 

Average 

25.9 

36.2 

44.6 

27.6 

37.7 

49.1 

100-Foot  Span  (10-Foot  Panels). 


14  
16 

29  3 
29  4 

42.5 
40  4 

51.8 
49  5 

31.5 
31  5 

45.0 
43  9 

57.8 
58  0 

18  
20  

31.8 
30.7 

42.5 
41  .6 

52.4 
52  8 

32.8 
32  3 

44.4 
46  2 

60.0 
60  0 

22  
24  

30.8 
31.6 

43.5 
43  0 

54.0 
54  2 

32.4 
33  4 

49.0 
49  2 

61.0 
61  0 

Average 

30.6 

42.6 

54.1 

32.3 

46.3 

59.6 

JUST    PUBLISHED. 

8vo,  Cloth,  Illustrated,  365  pages.          Price  $3.00  net. 

Earth  and  Rock  Excavation 

A  PRACTICAL  TREATISE. 


BY 


CHARLES  PRELINI,  C.E., 

AUTHOR   OF   "TUNNELINC," 

With  Tables,  and  many  Diagrams  and  Engravings. 


CONTENTS 

Preface,  Introduction.  Chapter  I. — Graphical  Representation  of  Earthwork ;  Plans 
and  Profiles.  II  — Methods  of  Calculating  Quantities  and  Cost  of  Earthwork.  III. — 
Cuts  and  Fills;  Borrow-pits  and  Spoil-banks.  IV. — Classification  of  Materials; 
Rock  Excavations  witho.it  Blasting.  V.— Excavation  of  Rock  by  Blasting;  the 
Drilling  of  the  Holes.  VI.— Rock  Excavation  by  Blasting;  Explosives  and  their 
Transportation  and  Storage.  VII. — Rock  Excavation  by  Blasting;  Fuses,  Firing 
and  Blasting.  VIII. — Earth  Excavation;  Hand-tools,  Machine  Excavation.  IX. — 
Earth  Excavation ;  Continuous  Digging-machines.  X. — Earth  Excavation ;  Inter- 
mittent Digging-machines.  XI. — Methods  of  Hauling  Excavated  Materials  on 
Level  Roads.  XII. — Hauling  Excavated  Materials  on  Horizontal  Roads.  XIII. — 
Method  of  Hauling  Excavated  Materials  on  Inclined  Roads.  XIV.— Vertical  Haul- 
ing or  Hoisting  of  Excavated  Materials.  XV. — Transporting  Excavated  Materials 
by  Aerialways.  XVI. — Transporting  Excavated  Materials  by  Cableways, 
XVII. — Transporting  Excavated  Materials  by  Telpherage.  XVIII.— Chains,  Ropes, 
Buckets,  Engines,  and  Motive  Power.  XIX. — Animal,  and  Mechanical  Labor. 
XX-XXI.— The  Direction  of  Excavation  Work.  XXII.— Shrinkage  of  Earth ; 
Cost  of  Earthwork.  XXIII.— Examples  of  Large  Canal  Excavation  Works.  Index. 


D.  VAN  NOSTRAND  COMPANY, 

Publishers  and  Booksellers, 

23  Murray  and  27  Warren  Sts.  NEW  YORK. 


TH I RD  EDITION,  REVISED. 

8vo.  Cloth,  31  I  Pages,  150  Illustrations.      -      -     Price,  S3.OO. 

TUNNELING: 

An  Exhaustive  Treatise,  containing  many  Working 
Drawings  and  Figures. 

BY 

CHAS.  PRELINI,  C.  E. 

WITH  ADDITIO-  S  BY 

CHARLES  5.  HILL,  C.  E. 

Associate  Editor  "Engineering  News." 


INTRODUCTION 
CHAP. 


III. 
IV. 
V. 
VI. 
VII. 

VIII. 
IX-XI. 


XII. 
XIII-XIV. 


XV. 

XVI. 

XVII. 

XV1II-XXI. 


XXII. 

XXIII. 

XXIV. 

XXV. 


Index. 


CONTENTS. 

— The  Historical  Development  of  Tunnel  Building. 

Preliminary  Considerations,  Choice  Between  a  Tunnel  and  an  Open 
Cut.  Method  and  Purpose  of  Geological  Surveys. 

Methods  of  Determining  the  Center  Line  and  Forms  and  Dimen- 
sions of  Cross-Section. 

Excavating  Machines  and  Rock  Drills ;  Explosives  and  Blasting. 

General  Methods  of  Excavation;  Shafts  :  Classification  of  Tunnels. 

Methods  of  Timbering  or  Strutting  Tunnels. 

Methods  of  Hauling  in  Tunnels. 

Types  of  Centers  and  Molds  Employed  in  Constructing  Tunnel  Lin- 
ings of  Masonry. 

Methods  of  Lining  Tunnels. 

Tunnels  Through  Hard  Rock;  General  Discussion;  Excavation  by 
Drifts.  Mont  Cenis  Tunnel:  The  Simplon  Tunnel:  St.  Gothard 
Tunnel:  Busk  Tunnel. 

Representative  Mechanical  Installations  for  Tunnel  Work. 

Excavating  Tunnels  Through  Soft  Ground;  General  Discussion; 
The  Belgian  Method:  The  German  Method:  Baltimore  Belt  Line 
Tunnel. 

The  Full  Section  Method  of  Tunneling;  English  Method;  Austrian 
Method. 

Special  Treacherous  Ground  Method;  Italian  Methodj  Quicksand 
Tunneling;  Pilot  Method. 

Open-Cut  Tunneling  Methods;  Tunnels  under  City  Streets.  Bos- 
ton Subway,  and  New  York  Rapid  Transit. 

Submarine  Tunneling:  General  Discussion:  The  Severn  Tunnel:  The 
East  River  Gas  Tunnel ;  The  Van  Buren  Street  Tunnel,  Chicago 
The  Milwaukee  Water- Works  Tunnel :  The  Shield  System. 

Accidents  and  Repairs  in  Tunneling  during  and  after  Construction. 

Relieving  Timber-Lined  Tunnels  with  Masonry. 

Ventilating  and  Lighting  of  Tunnels  during  Construction. 
Cost  of  Tunnel  Excavation,  and  the  Time  required  for  the  work. 


D.  VAN  IMOSTRAIMD  COMPANY, 

Publishers  and  Booksellers, 
23  Murray  <ma  27  Warren  Sts. ,  NEW  YORK. 


Jxist  Published 

8vo.  Cloth,  Illustrated,  122  pp.  Price,    $1:32    Net 

EXPERIMENTS 

ON    THE 

FLEXURE  of  BEAMS, 

RESULTING    IN    THE 

DISCOVERY  OF   NEW  LAWS 
OF  FAILUR.E  BY  BUCKLING 

BY 

ALBERT  E.  GUY 

Reprinted  from  the  "AMERICAN  MACHINIST" 

THE  analogy  of  the  failure  of  the  compression  side  of  a  beam  by  buckling,  to  the 
method  of  failure  of  a  long  column  was,  of  course,  long  ago  remarked,  but  we 
believe  there  has  been  no  previous  attempt — certainly  no  successful  attempt — to 
connect  the  two  by  a  formula.     Mr.  Guy's  experiments  have  been  successful  beyond  any 
reasonable  expectation  in  connecting  them,  and  in  showing  that  Euler's  formula  for  long 
columns  is,  in  fact,  the  fundamental  formula  which  lies  at  the  base  of  the  whole  subject. 
We  believe  there  is  not  in  any  existing  text-book,  a  formula  by  which  the  strength 
CH  a  long  beam  unsupported  sideways,  may  be  determined.     Mr.  Guy  discloses  the  laws" 
of  failure  in  this  manner,  for  the  first  time,  and  they  are  in  consequence,  entitled  to  be 
!  called,  as  we  shall  hereafter  call  them,  Guy's  laws.     The  disclosure  of  such  laws  alone 
i  would  be  a  notable  achievement,  but  when  to  this  is  added  the  connection  through 
definite  formulas  of  long  beams  and  columns,  including  inclined  beams  acted  upon  by 
vertical  forces,  the  accomplishment  is  nothing  less  than  brilliant. 

—Extracts  from  Preface. 

CONTENTS 

INTRODUCTION 

A  SIMPLE  PROBLEM 

THE  TRANSVERSE  SHEARING 
THE  LONGITUDINAL  SHEARING 
THE  DEFLECTION  OF  THE  BEAM 
EXPERIMENTS 
COROLLARY 

THAT  SIMPLE  PROBLEM 

THE  BEST  FORM  OF  SECTION 
THE  CENTRAL  WEB 

THE  WIDTH  OF  THE  SECTION 
EXAMPLE 
SOLUTION 

THE  SHAPE  OF  THE  BEAM 
THE  NEW  LAW 
FIRST  EXAMPLE 
SECOND  EXAMPLE 

D.    Van     Nostrand     Company 

Publishers   and   Booksellers    V>    23    Murray   Street  and 
27  Warren  Street,  New  York 


JUST  PUBLISHED. 

8vo.  Cloth,  174  Pages,  Illustrated,  Price  $2.00,  Net, 

THE 

STATICALLY-INDETEEHINATE 

STRESSES 

IN  FRAMES  COMMONLY  USED  FOR 

BRIDGES 

BY 

ISAM!  HIROI,  C.  E.,  Dr.  Eg., 

Professor  of  Civil  Engineering  in  the  College  of  Engineering  Tokyo  Imperial  University. 


EXTRACT  FROM  PREFACE. 

The  present  work  is  the  outgrowth  of  a  series  of  lectures  given 
to  the  students  of  CiviJ  Engineering  in  the  Tokyo  Imperial  Univer- 
sity. It  contains  the  solution  of  those  problems  most  commonly  met 
in  the  practice  of  a  bridge  engineer,  the  aim  of  the  author  being  to 
save  time  and  labor  of  those  intent  on  a  more  rational  design  of  the 
class  of  the  structures  treated,  than  is  generally  followed,  by  furnish- 
ing them  with  necessary  formulas  for  which  rough  approximation  or 
even  guess-work  frequently  forms  a  substitute. 

INTRODUCTORY  CHAP.-Qeneral  Principles. 
CHAP.  I.— Trussed  Beams. 
CHAP.  II.— Viaduct  Bents. 
CHAP.  III.— Continuous  Girders. 
CHAP.  IV.— Arches  with  Two  Hinges. 
CHAP.  V.— Arches  without  Hinges. 
CHAP.  VI.— Suspension  Bridges.    Trusses  with 

Redundant  Members. 

CHAP.  VII.— Secondary  Stresses  due  to  rigid= 
ity  of  Joints. 

D.  VAN  NOSTRAND  COMPANY, 

Publishers  and  Booksellers, 

23  Mwrray  and  27  Warren  Streets,         -        -         NEW  YORK. 


JUST  PUBLISHED. 

4to,  7%  x  11,  Cloth,  530  pages,  511  illustrations.   Price  $7.00  net. 

Reinforced  Concrete 

BY 

CHARLES  F.  MARSH 

Assoc.  M.  Inst.  C.  B.,  Assoc.  M.  Inst.  M.  E. 

With  many  Tables,  Diagrams  and  Engravings 

CONTENTS: 

General  View  of  the  Subject.    Systems  Employed.    Ma- 
terials.    Practical  Construction.     Experimental  Re- 
search and  Data  Deduced  Therefrom.       Calcu- 
lations.    Some  Structures  which  have  been 
Erected  in  Reinforced  Concrete.  Appendix. 

INTRODUCTION 

In  the  following  pages  the  author  has  endeavoured  to  place  before 
engineers,  architects,  and  others,  a  complete  treatment  of,  the 
subject  of  reinforced  concrete,  in  so  far  as  is  possible  at  the  present 
day. 

All  the  subject  matter  has  been  so  arranged  as  to  facilitate 
reference  as  much  as  possible,  and  the  several  systems  used  up  to 
the  present  have  been  placed  in  alphabetical  order,  so  that  any 
particular  one  may  be  readily  found  when  desired. 

It  is  believed  that  the  part  relating  to  the  calculations,  covers 
all  forms  of  construction  in  as  concise  and  clear  a  manner  as 
possible.  The  formulae  for  slabs  and  beams,  although  giving  some- 
what smaller  dimensions  than  those  recommended  by  M.  Christophe 
in  Le  Beton  Arme  (a  standard  French  work  on  the  subject),  are 
still  well  on  the  side  of  safety,  and  it  is  hoped  that  the  tables  and 
diagrams  may  be  of  use  in  saving  the  labour  necessary  in  making 
the  requisite  calculations.  The  subject  of  arches  has  been  dealt 
with  in  as  condensed  a.  form  as  possible,  compatible  with  a  clear 
demonstration  of  the  methods  adopted  for  locating  the  pressure 
curve.  The  graphical  method  -for  finding  the  stresses  to  be  resisted 
in  domed  coverings,  is  believed  to  be  entirely  new  and  greatly 
simplifies  the  treatment  of  these  structures. 

It  has  been  considered  advisable  to  illustrate  the  book  Very  fully, 
in  order  that  all  the  subject  matter,where  possible,  may  be  rendered 
clearer,  and  that  a  true  idea  may  be  formed  of  the  remarkable 
adaptability  of  reinforced  concrete  for  constructural  purposes. 

D.  VAN  NOSTRAND  COMPANY 

Publishers  and  Booksellers 

*3  HURRAY  AND  37  WARREN  STREETS,  NEW  YORK. 


FOURTH      EDITION,     REVISED     AND     ENLARGED. 
16mo.  Cloth,  212  Pages,  Illustrated.     Price  50  cents, 

THEORY   OF 

STEEL = CONCRETE    ARCHES 

AND    OF 

VAULTED  STRUCTURES 

BY 

WILLIAM    CAIN, 

Member  Am.  Soc.  C.  B.,  Prof,  of  Mathematics,  University  of  North 
Carolina. 


CONTENTS. 

CHAP,  i.— Arches  of  Variable  Section  under  Vertical  Loads.  — In- 
troductory—  Formulas  for  unit  stress  for  a  steel-concrete  arch  —  Con- 
ditions for  equilibrium  for  arch  with  no  hinges  — Deflection  at  the 
crown --Division  of  the  neutral  axis  — Complete  graphical  treatment  for 
a  steel-concrete  arch  with  partial  load  — Arch  loaded  with  its  own 
weight  — Demonstration  — Unit  stresses,  etc.— Temperature  stresses- 
Properties  of  Concrete  — Change  of  span  — Arch  hinged  at  end  only- 
Abutments— Spandrel  resistance  for  Voussoir  arches  — Methods  of 
failure  of  arches  — Height  of  surcharge  for  equilibrium. 

CHAP.  II.— Culverts  and  Tunnel  Arches.  — Formulas  for  passing 
a  line  of  resistance  through  three  given  points  — Application  to  cul- 
verts—Tunnel arches  — The  ellipse,  the  proper  form  for  a  tunnel  arch. 

CHAP.  III.  — Groined  and  Cloistered  Arches.  — Groined  arch- 
Evaluation  of  thrusts  — Formulas  for  volume  — Arch  of  groin  and 
abutment  — Cloistered  arch. 

CHAP.  IV.  — Domes  of  Masonry.  —  Forces  acting  — Example  of  a 
dome  with  backing  —  Formulas  for  volume  —  Dome  of  two  shells 
with  lantern  —  Tensions  in  iron  bands  — Thrusts  —  Dome  without 
lantern  —  Suggestion  —  Reinforced  concrete  on  metal  dome  —  Open 
spherical  dome  with  lantern  —  Spherical  dome  — Analytical  theory  — 
Conical  dome  —  Graphical  treatment  —  Conical  dome  —  Analytical 
theory. 

APPENDIX.— Resume  of  operations  for  arch. 


D.  VAN  NOSTRAND  COMPANY, 

Publishers   and   Booksellers, 
23  Murray  and  27  WajgE*fc«a«.     •      •     NEW  YORK. 


RETURN  TO  the  circulation  desk  of  any 
University  of  California  Library 

or  to  the 

NORTHERN  REGIONAL  LIBRARY  FACILITY 
Bldg.  400,  Richmond  Field  Station 
University  of  California 
Richmond,  CA  94804-4698 

ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 

•  2-month  loans  may  be  renewed  by  calling 
(510)642-6753 

•  1-year  loans  may  be  recharged  by  bringing 
books  to  NRLF 

•  Renewals  and  recharges  may  be  made  4 
days  prior  to  due  date. 

DUE  AS  STAMPED  BELOW 


DEC  15 1999 


12,000(11/95) 


! 101 


